It's a piece of cake - assuming you're running OS 10.5 (Leopard) and that your Mini is connected to the internet via ethernet, here's what you do:
- Open System Preferences
- Go to "Sharing"
- In the list on the left, select (but don't check the box next to) "Internet Sharing"
- Share connection from: Ethernet
- To computers on: Airport
- If you'd like, you can set up a password to access your network, but I've found that Windows machines have trouble accessing the network if it's password protected, even when following the 5 or 13 character guideline
- Check the box next to "Internet Sharing" and you're good to go. The Airport icon on your menu bar should appear to have an arrow on it, and your computer's name should show up on her laptop's list of available networks
In this case, the Mini acts as your wireless router so you don't need one, you just need to leave the Mini running. I share my Mini's ethernet connection with my iPod Touch (Pandora anywhere in the house) and my work laptop without a problem.