How do I set up different tab settings for different languages in Vim?

These other answers seem way too complex. Instead of messing around with yet more directories and files in your ~/.vim tree, just add the following to your ~/.vimrc.

autocmd Filetype python setlocal expandtab tabstop=4 shiftwidth=4 softtabstop=4

(you can be l33t and abbreviate parameters to et ts=4 sw=4 sts=4). I found this in
Setting Vim whitespace preferences by filetype