Do not attempt to install OBSE with the Nexus Mod manager - it won't work!
The instructions for installing and running OBSE differ based on whether you are using a retail or Steam version of the game.

Retail (Non-Steam) version
1. Copy obse_1_2_416.dll, obse_editor_1_2.dll, and obse_loader.exe to your Oblivion directory. This is usually in your Program Files folder, and should contain files called "Oblivion.exe" and "OblivionLauncher.exe".
2. Run oblivion by running obse_loader.exe from the Oblivion directory.

If you use a desktop shortcut to launch Oblivion normally, just update the shortcut to point to obse_loader.exe instead of oblivion.exe.

Steam version
1. Copy obse_1_2_416.dll, obse_editor_1_2.dll, and obse_steam_loader.dll to your Oblivion directory. This is usually "C:Program FilesValveSteamSteamAppscommonoblivion".
2. Ensure you have enabled the Steam community in-game, or OBSE will fail to load. Go to Steam > Settings > In-Game and check the box marked "Enable Steam Community In-Game".
3. Launch Oblivion via Steam or by running Oblivion.exe. OBSE will automatically be run along with Oblivion when launched. To disable this, rename or move obse_steam_loader.dll. You do not need to use obse_loader.exe unless you are running the editor.

Direct2Drive or GameStop App (Impulse) version
Not possible.