:set tabstop=4
:set shiftwidth=4
:set expandtab
This will insert four spaces instead of a tab character. Spaces are a bit more “stable”, meaning that text indented with spaces will show up the same in the browser and any other application.
To make the change for one session, use this command:
:set tabstop=4
To make the change permanent, add it to ~/.vimrc or ~/.vim/vimrc:
set tabstop=4
This will affect all files, not just css. To only affect css files:
autocmd Filetype css setlocal tabstop=4
as stated in Michał’s answer.