If you are brand-new to Oblivion mods or just looking for a clean start, use this guide to learn how to set up Oblivion for mod use. If you already have the game installed, re-installing clean is optional; I have simply found this method to be the best way to prevent problems in the future.
This guide was written for Oblivion, but also mostly works for Skyrim. I'll add a second guide specifically for Skyrim once there are more mods and utilities out for it. Meanwhile, just improvise with the instructions here.

Step 1: Install Oblivion and any expansions and official mod packs you have for it.
If you are running Windows Vista or later, make sure to install Oblivion OUTSIDE of the Program Files directory. Many choose c:Oblivion, or c:GamesOblivion, as their alternate install location. This prevents you from needing to run as Administrator or turn off UAC for mods to work.
Step 2: Download and install the Official Oblivion Patch.
Your game MUST be patched to the latest (v1.2.0416) in order for most mods to work. Make sure you choose the Shivering Isles patch if you have that expansion.
If you are installing the Game of the Year version with Shivering Isles, your game will already be patched. Attempting to patch it will result in error messages.

Step 3: Download and install the Unofficial Oblivion Patch (UOP), as well as the Unofficial Shivering Isles Patch (USIP) and the Unofficial Official Mods Patch (UOMP) if you have installed those components.
These patches correct many errors and inconsistencies in the game that Bethesda couldn't be bothered to fix on their own. The corrections prevent crashes, immersion breaking inconsistencies, and fix literally thousands of tiny and monstrous bugs in the game.
These patches replace a large amount of models and textures. Therefore, it is wise to install these before any other mesh or texture packs.
Step 4: Download and install OBSE.
Oblivion Script Extender (OBSE) provides a plethora of scripting functions for modders. As a player, you need to have this installed so mods that rely on these functions work properly for you.
Step 5: Download and install Pluggy.
Pluggy extends OBSE even further. Like with OBSE, you will see no changes in-game; this simply allows you to use mods that depend on it.
Step 6: Set up multiple Oblivion installs using MOM or mTES4.
This step is completely optional, but now is the best time to do it if you're gonna! Many mod users enjoy having multiple installs so they can have completely different mod setups for different characters, or for testing/mod-making, or to run a Total Conversion (where Oblivion gets replaced by a different game built on the same engine, such as Nehrim). It also makes a nice backup system. For the particular instructions on this, please see the documentation for the applications linked above.
I heavily recommend that you make a clone of your install before you start loading it up with mods or even mod managers, other than the ones listed above. This way you always have one 'clean' install, which you can use to test mods, to make mods, or even to fall back on should one of your modded installs go absolutely haywire.
Note that you will need to adjust the settings of mod managers so that they store mod packages in separate folders, unless you want all of your installs to use the same mod packages (OBMM settings button, Wrye Bash's bash.ini). MOM and mTES4 can set this up for you too, if you prefer not to do it manually.
Step 7: Choose a mod manager. Download & install it.
This step is big. The two main contenders here are Oblivion Mod Manager and Wrye Bash. I use both for different things, and you eventually will too. The key differences:
OBMM is much simpler for a new mod user. When you download a mod in *.omod format, you can just double-click it from within Explorer, and OBMM will open and the mod will be in list, ready to be activated. Double-clicking it again from within OBMM will activate the mod. All the files will go in the right place. When you de-activate the mod, all those files will be removed, making cleanup super easy. Modders can even add scripts to omods to present you with the mod's options when you activate the omod. You can create your own .omod files from any folder or archive easily. OBMM also handles archive invalidation for you.
Wrye Bash is a laden trove of useful and, in some cases, necessary features for mod users. It manages not just your mods, but your saved games too! Its main claim to fame, however, is the Bashed Patch - a mod built on the spot by the program that functions as a patch for your existing mods to help them all work together seamlessly. Without a Bashed Patch, many mods can't work together, and you'd have to choose one or the other, or manually merge the mods into one.
My recommendation is to start with OBMM. Learn it. Get comfortable using and making omods. After a while you'll start to realize you need a Bashed Patch, because you can't have one mod adding new eyes and another mod adding new hairs and have both of them work without one (that's one example of thousands). When you get to that point, it's time to delve into Wrye Bash.
If you feel you're ready to start with Wrye Bash now, or you're determined to use mods that you already know require it, then the place to start is alt3n1ty's Wrye Bash Pictorial Guide.
Step 8: Back up your Oblivion installation.
By this I mean copy and paste the ENTIRE thing into wherever you keep backup data. If you screw up your game really badly with mods, you won't have to repeat steps 1-5 to start over. You can literally just delete your current Oblivion folder, then copy and paste this backup folder into its former place. You probably won't need the backup once you get really comfortable with the game's file & folder structure, at which point you can delete the backup. You can also skip this step if you're really confident, or just low on disk space.
Once you have a mod setup you really like, you may want to do this a second time, depending on how much hard drive space you have to spare.
If you set up multiple installs for Oblivion, you can skip all of this, since you've pretty much already done it.

Step 9: Download and install mods!
Start small and simple at first if you've never used mods before. Avoid anything that appears complicated to install, or complicated to play.
If a mod's description says, 'Requires X to work,' then don't download or install it unless you actually have X.
If a mod's description says, 'Is not compatible with X,' then don't download or install it if you have X.
One or two at a time. Installing a lot of mods at once takes away the fun of the discovery, and also pretty much guarantees you're going to break something without knowing how you did it. But once you've learned the ropes, you'll find that mods bring a ton of enrichment to the game and can extend its enjoyable play-through time by hundreds of hours.
Happy gaming!

If you are brand-new to Oblivion mods or just looking for a clean start, use this guide to learn how to set up Oblivion for mod use. If you already have the game installed, re-installing clean is optional; I have simply found this method to be the best way to prevent problems in the future.
This guide was written for Oblivion, but also mostly works for Skyrim. I'll add a second guide specifically for Skyrim once there are more mods and utilities out for it. Meanwhile, just improvise with the instructions here.

Step 1: Install Oblivion and any expansions and official mod packs you have for it.
If you are running Windows Vista or later, make sure to install Oblivion OUTSIDE of the Program Files directory. Many choose c:Oblivion, or c:GamesOblivion, as their alternate install location. This prevents you from needing to run as Administrator or turn off UAC for mods to work.
Step 2: Download and install the Official Oblivion Patch.
Your game MUST be patched to the latest (v1.2.0416) in order for most mods to work. Make sure you choose the Shivering Isles patch if you have that expansion.
If you are installing the Game of the Year version with Shivering Isles, your game will already be patched. Attempting to patch it will result in error messages.

Step 3: Download and install the Unofficial Oblivion Patch (UOP), as well as the Unofficial Shivering Isles Patch (USIP) and the Unofficial Official Mods Patch (UOMP) if you have installed those components.
These patches correct many errors and inconsistencies in the game that Bethesda couldn't be bothered to fix on their own. The corrections prevent crashes, immersion breaking inconsistencies, and fix literally thousands of tiny and monstrous bugs in the game.
These patches replace a large amount of models and textures. Therefore, it is wise to install these before any other mesh or texture packs.
Step 4: Download and install OBSE.
Oblivion Script Extender (OBSE) provides a plethora of scripting functions for modders. As a player, you need to have this installed so mods that rely on these functions work properly for you.
Step 5: Download and install Pluggy.
Pluggy extends OBSE even further. Like with OBSE, you will see no changes in-game; this simply allows you to use mods that depend on it.
Step 6: Set up multiple Oblivion installs using MOM or mTES4.
This step is completely optional, but now is the best time to do it if you're gonna! Many mod users enjoy having multiple installs so they can have completely different mod setups for different characters, or for testing/mod-making, or to run a Total Conversion (where Oblivion gets replaced by a different game built on the same engine, such as Nehrim). It also makes a nice backup system. For the particular instructions on this, please see the documentation for the applications linked above.
I heavily recommend that you make a clone of your install before you start loading it up with mods or even mod managers, other than the ones listed above. This way you always have one 'clean' install, which you can use to test mods, to make mods, or even to fall back on should one of your modded installs go absolutely haywire.
Note that you will need to adjust the settings of mod managers so that they store mod packages in separate folders, unless you want all of your installs to use the same mod packages (OBMM settings button, Wrye Bash's bash.ini). MOM and mTES4 can set this up for you too, if you prefer not to do it manually.
Step 7: Choose a mod manager. Download & install it.
This step is big. The two main contenders here are Oblivion Mod Manager and Wrye Bash. I use both for different things, and you eventually will too. The key differences:
OBMM is much simpler for a new mod user. When you download a mod in *.omod format, you can just double-click it from within Explorer, and OBMM will open and the mod will be in list, ready to be activated. Double-clicking it again from within OBMM will activate the mod. All the files will go in the right place. When you de-activate the mod, all those files will be removed, making cleanup super easy. Modders can even add scripts to omods to present you with the mod's options when you activate the omod. You can create your own .omod files from any folder or archive easily. OBMM also handles archive invalidation for you.
Wrye Bash is a laden trove of useful and, in some cases, necessary features for mod users. It manages not just your mods, but your saved games too! Its main claim to fame, however, is the Bashed Patch - a mod built on the spot by the program that functions as a patch for your existing mods to help them all work together seamlessly. Without a Bashed Patch, many mods can't work together, and you'd have to choose one or the other, or manually merge the mods into one.
My recommendation is to start with OBMM. Learn it. Get comfortable using and making omods. After a while you'll start to realize you need a Bashed Patch, because you can't have one mod adding new eyes and another mod adding new hairs and have both of them work without one (that's one example of thousands). When you get to that point, it's time to delve into Wrye Bash.
If you feel you're ready to start with Wrye Bash now, or you're determined to use mods that you already know require it, then the place to start is alt3n1ty's Wrye Bash Pictorial Guide.
Step 8: Back up your Oblivion installation.
By this I mean copy and paste the ENTIRE thing into wherever you keep backup data. If you screw up your game really badly with mods, you won't have to repeat steps 1-5 to start over. You can literally just delete your current Oblivion folder, then copy and paste this backup folder into its former place. You probably won't need the backup once you get really comfortable with the game's file & folder structure, at which point you can delete the backup. You can also skip this step if you're really confident, or just low on disk space.
Once you have a mod setup you really like, you may want to do this a second time, depending on how much hard drive space you have to spare.
If you set up multiple installs for Oblivion, you can skip all of this, since you've pretty much already done it.

Step 9: Download and install mods!
Start small and simple at first if you've never used mods before. Avoid anything that appears complicated to install, or complicated to play.
If a mod's description says, 'Requires X to work,' then don't download or install it unless you actually have X.
If a mod's description says, 'Is not compatible with X,' then don't download or install it if you have X.
One or two at a time. Installing a lot of mods at once takes away the fun of the discovery, and also pretty much guarantees you're going to break something without knowing how you did it. But once you've learned the ropes, you'll find that mods bring a ton of enrichment to the game and can extend its enjoyable play-through time by hundreds of hours.
Happy gaming!