As has been pointed out in a couple of other answers, the preferred method now is NOT to use smartindent, but instead use the following (in your .vimrc):
filetype plugin indent on
” show existing tab with 4 spaces width
set tabstop=4
” when indenting with ‘>’, use 4 spaces width
set shiftwidth=4
” On pressing tab, insert 4 spaces
set expandtab
In your [.vimrc:][1] file:
set smartindent
set tabstop=4
set shiftwidth=4
set expandtab
The help files take a bit of time to get used to, but the more you read, the better Vim gets:
:help smartindent
Even better, you can embed these settings in your source for portability:
:help auto-setting
To see your current settings:
:set all
As graywh points out in the comments, smartindent has been replaced by cindent which “Works more cleverly”, although still mainly for languages with C-like syntax:
:help C-indenting
Related, if you open a file that uses both tabs and spaces, assuming you’ve got
set expandtab ts=4 sw=4 ai
You can replace all the tabs with spaces in the entire file with
:%retab