Vim Insert Mode on Mac OS X

Vim enters the insert mode using i (or a for append), regardless of platform. Overwrite mode is only rarely entered using Shift+r. I've never used the Insert key here.

If this is as simple a question as it seems, you merely press i.

The other use of the Insert key is to switch between replace-mode and insert-mode when already in either. You can accomplish this easily on the Mac by just mapping another key to do this for you. In your ~/.vimrc just put imap <F13> <Insert> and now the F13 key (which on my Mac keyboard is the closest key to where the Insert key is on a regular keyboard).