What is Body Shop?
The Sims 2 Body Shop is a program created by Maxis that allows users to create new textures for sim-related content like skintones, hair, clothing, makeup, eyes, etc.
Where to get Body Shop
Body Shop installs with the game itself - if you have the game installed, you have Body Shop. There was also a version of Body Shop that was downloadable, distributed before the game's release, but you do not need or want this version if you have the game installed. It does not contain all the same content as the game itself (only some basic starter packs), does not take custom content whatsoever, and creates broken skintones. If, for some reason, you simply must have the downloadable Body Shop, you can get it here and a starter pack of content for it here.
If you have expansions installed, you should use the Body Shop shortcut from the latest installed expansion to run Body Shop. For example, if the latest expansion you have is Nightlife, you should use the "Start - Programs - EA Games - The Sims 2 - The Sims 2 Nightlife - The Sims 2 Body Shop" shortcut to start Body Shop.
The Pets Expansion and Body Shop
The version of Body Shop that installs along with the Pets expansion contains certain flaws that cause most of the content made with Pets Body Shop to work incorrectly for users without Pets. Items will show up as naked full body sim thumbnails regardless of type, and will not work properly. Maxis has released a patch which fixes this problem. You can get the patch here: http://thesims2.ea.com/help/index.php?pid=Help
Pets Body Shop also now packages custom meshes for any custom clothing or hair a sim may be wearing when it packs a sim. This has not been corrected with the Body Shop patch. You can find instructions on removing the included meshes here: http://www.modthesims2.com/article.php?t=202512
There is a script, in the R programming language, that loops through all package files and detects which were wrong. See in Detect Pets Body Shop bug/Source Code.
Body Shop Issues
Is Body Shop making all your creations blurry? Try this: http://www.modthesims2.com/article.php?t=147242
Is Body Shop crashing, not running, or otherwise acting badly? Look here: http://www.modthesims2.com/article.php?t=177332