You'll need to create a computer to computer network.
Select "Create Network..." from the Airport menu on the computer that has the file you want to share and click ok to create the computer to computer network. You'll see the name for the sharing computer which should be your user name by default. Set up file sharing as described in taylorwilsdon's post.
On the machine that will connect to the file sharing computer, select the Airport menu and you should see the name of the sharing computer momentarily (after it finishes scanning). Select it and you should be good to go. You'll see your sharing computer in the finder sidebar.