I wrote all about tabs in vim, which gives a few interesting things you didn't ask about. To automatically indent braces, use:
:set cindent
To indent two spaces (instead of one tab of eight spaces, the vim default):
:set shiftwidth=2
To keep vim from converting eight spaces into tabs:
:set expandtab
If you ever want to change the indentation of a block of text, use < and >. I usually use this in conjunction with block-select mode (v, select a block of text, < or >).
(I'd try to talk you out of using two-space indentation, since I (and most other people) find it hard to read, but that's another discussion.)
A lot of vim's features (like autoindent and cindent) are turned off by default. To really see what vim can do for you, you need a decent ~/.vimrc.
A good starter one is in $VIMRUNTIME/vimrc_example.vim. If you want to try it out, use
:source $VIMRUNTIME/vimrc_example.vim
when in vim.
I'd actually suggest just copying the contents to your ~/.vimrc as it's well commented, and a good place to start learning how to use vim. You can do this by
:e $VIMRUNTIME/vimrc_example.vim
:w! ~/.vimrc
This will overwrite your current ~/.vimrc, but if all you have in there is the indent settings Davr suggested, I wouldn't sweat it, as the example vimrc will take care of that for you as well. For a complete walkthrough of the example, and what it does for you, see :help vimrc-intro.
Note that it advises against using "set autoindent." The best feature of all I find in this explanation is being able to set per-file settings, which is especially useful if you program in python and C++, for example, as you'd want 4 spaces for tabs in the former and 2 for spaces in the latter.