How to use and access web sharing with Mac OS X Lion?
Web Sharing opens port 80 (http) on your machine and points any incoming requests to ~/Sites. You'll want to put your PHP app there for it to work through Web Sharing. I'm not sure if there is any further configuration you have to do on the PHP/MySQL side since I don't know anything about either of those languages. That's probably a question for SuperUser.

As far as accessing it remotely, you'll need to open port 80 on your router and point it to your computer's internal IP address. Then you'll want to give your friend either your domain name or your current IP address from your ISP and have them type it in their web browser.