BAIN is an automated mod installer which is part of Wrye Bash. Use the Wizard install for easier process (right click on the archive and select Wizard).
Download all files labelled REQUIRED. There will typically be two files to download: "Better Cities" and "Better Cities Primary Resources"
At the end you should have five BSAs from Better Cities, one ESM, an ESP named "Better Cities .esp" and various other ESPs depending on the choices you made. If you have less than five BSAs, then you installed the mod wrong.
If you want more information about what a specific ESP in the BC archive does, then read What Does Each File Do.
If updating from an older version, please ensure that you uninstall the old version before installing the new version.
Simply place the two downloaded archives into the "Oblivion Mods\Bash Installers\" folder, then go to the Installers tab in Wrye Bash and run the Wizard on each archive and answer each query.
You must have 5 BSA installed.
Adjust your load order so that all Better Cities ESPs are near the end of your load order. All Replacer ESPs should be BEFORE the Better Cities ESPs. All Better Cities Patches should be AFTER the Better Cities ESPs, starting with the FPS patches, then the compatibility patches. Highly recommend using BOSS (Better Oblivion Sorting Software) for this.