Using MacMini to Broadcast Wireless

You can activate it through the Sharing preferences pane. Open System Preferences, click on Sharing, click on Internet Sharing. Change the "Share Your Connection" to Ethernet, and then activate the Airport check box below. Also, click on the Airport Options to set up your SSID and WEP key. And finally when all of that is done find the checkbox in the left-most column showing all the sharable services and click Internet sharing to On.

The airport options that you can set in internet sharing are kind of limited, and I don't believe it lets you hide the SSID. Maybe there is a way to do that via plist editing, but in the long run it doesn't matter. The bad guys intent on poaching your wireless connection will see it whether or not the SSID is hidden.