How do I install MacVim?
Here is the procedure I recommend, for those who are comfortable with the command-line and with Homebrew:

Install Homebrew.

Run the following on the command line (in Terminal):

brew install macvim --with-override-system-vim
brew linkapps


Edit your shell startup files to ensure that /usr/local/bin comes first in your $PATH.

If you use vim as $VISUAL or $EDITOR, add `export VISUAL='mvim -f' to your environment (details).

Check that you installed everything correctly by running

brew doctor


Now, you can run the graphical MacVim on a file by running mvim foo.txt from the command-line.  Or, you can run the text-based editor by running vim foo.txt.  Also, if other programs (e.g., git) fork off a separate editor, they'll run the graphical MacVim.

See also How to run mvim (MacVim) from Terminal? and Set macvim as default application after homebrew installation.