How do I change tab size in Vim?

Expanding on zoul’s answer:

If you want to setup Vim to use specific settings when editing a particular filetype, you’ll want to use autocommands:

autocmd Filetype css setlocal tabstop=4

This will make it so that tabs are displayed as 4 spaces. Setting expandtab will cause Vim to actually insert spaces (the number of them being controlled by tabstop) when you press tab; you might want to use softtabstop to make backspace work properly (that is, reduce indentation when that’s what would happen should tabs be used, rather than always delete one char at a time).

To make a fully educated decision as to how to set things up, you’ll need to read Vim docs on tabstop, shiftwidth, softtabstop and expandtab. The most interesting bit is found under expandtab (:help 'expandtab):

There are four main ways to use tabs in Vim:

1. Always keep ‘tabstop’ at 8, set ‘softtabstop’ and ‘shiftwidth’ to 4 (or 3 or whatever you prefer) and use ‘noexpandtab’. Then Vim will use a mix of tabs and spaces, but typing and will behave like a tab appears every 4 (or 3) characters.
2. Set ‘tabstop’ and ‘shiftwidth’ to whatever you prefer and use ‘expandtab’. This way you will always insert spaces. The formatting will never be messed up when ‘tabstop’ is changed.
3. Set ‘tabstop’ and ‘shiftwidth’ to whatever you prefer and use a |modeline| to set these values when editing the file again. Only works when using Vim to edit the file.
4. Always set ‘tabstop’ and ‘shiftwidth’ to the same value, and ‘noexpandtab’. This should then work (for initial indents only) for any tabstop setting that people use. It might be nice to have tabs after the first non-blank inserted as spaces if you do this though. Otherwise aligned comments will be wrong when ‘tabstop’ is changed.