There is also a radio button on the Network Connection tab marked Connect to network through modem. Use this option if your only network connection is via dialup. Yes, it's very slow, but at least you're wireless. Note that the dialup and Ethernet choices are exclusive, and can't be used at the same time.
When you check Connect to network through modem, the pane prompts you for phone number, modem init string, and other dialup-related fields. Make sure that Automatic dialing is checked, so it will dial the phone when you start using the AirPort. Click on the Username/Password/Login Script button to enter your login information. On this screen, you can also define a custom login script, if you need to. The default script has worked fine for me with a couple of different ISPs.
Once the AirPort is configured for dialup, it will dial the phone and connect any time it senses Internet traffic on the wireless port. Just start using your wireless card as usual, and after an initial delay (while it's dialing the phone), you're online.