How do I monitor the Airport base station currently used for wifi?
timothymh's solution is definitely the simplest if you just need to know occasionally, and is built-in, but if you need something more advanced (e.g. monitoring), then the following may be useful:


iStumbler (free), though I'd recommend the latest beta if you're on a recent version of OS X
KisMAC (free)
inSSIDer (about $5)


From the screenshots, inSSIDer actively displays which network you're currently connected to, but otherwise all three show lots of details of all networks your card can pick up, including channels, signal strength and BSSIDs.

If your aim is to test the coverage of wifi access points, you will probably find more benefit from something like NetSpot (free). This lets you map the signal strength as a 'heat map' in your home/office/etc, effectively letting you see where each/any access point is available from, where you will/won't get access, and how strong the signal will be.

Edit:
To monitor AP switching, using the terminal, it is possible to watch the system logs:

tail -F /var/log/system.log | grep BSSID


Or simply use the console: Applications > Utilities > Console. In the filter write BSSID and you will see when your computer switches across BSSIDs.