Connecting iPhone to AirPort Extreme

While you're at home (i.e. within the network), on your iPhone, go to settings, Wi-Fi. Make sure wi-fi is set to on. The phone should scan for networks, find yours, and let you join it. Make sure Ask to Join Networks is on too.

From then on, the phone should automatically pick up the wi-fi network when you are at home

Please excuse me if this is a dumb question, but I'm still a newbie to the MAC world.

I too am trying to figure out if I can connect directly to my Mac Mini from my iPhone via the AirPort utility. Is this possible, or do I have to connect via a wireless router?

In order to connect your mac mini to your iphone, so to speak, you must be connecting your mac mini over ethernet.
you have to enable internet sharing in the system preferences > sharing. Once done, click on the Wifi indicator in the menu bar and choose "create network". Give it a name and create it, then with your iphone, go to settings > wifi and join the network you've just created. Voila, internet from your mac mini to your iphone wirelessly. Range is somewhat limited, of course.

Answer: you do not have to connect via a wireless router.

That sure was easy!

Thanks!!!!