How can I reset Vim back to a plain vanilla install?

cd
mv .vimrc .vimrc-old
mv .vim .vim-old
touch .vimrc
mkdir .vim

To remove everything from your vim configuration remove the entire .vim folder as well as everything from your .vimrc file. Keep the empty file in place though because without it vim will start in compatible mode by default and you almost certainly don't want that.

Note that there are system-wide files that are not stored in your home directory but if you haven't tweaked any of those then the above steps are all you need to do.