I am not quite clear why you are trying to get wireless going? If it's not necessary to your setup, I would try to get a wired connection working first.
But to go over both: for the wired connection, I would choose the "test" option first, and then if it succeeds, try the "Auto DHCP" option.
For wireless, it should have autodetected the card (unfortunately for this test, mine was able to even though it is one of the annoying Broadcom cards), but if it didn't, you can try to find the matching driver.
Assuming that you get to the point that you do have a wireless driver up, then the process is very similar to that of wired connections. Click on the interface button, but then choose the "wireless" button. Enter any access point information that you need to (encryption or SSID, for instance) and then hit the "Scan" button. Choose your wireless network, and then use the "Back" button. Now, like the wired connection, do a "Test" and then an "Auto DHCP".
(Two gotchas that slowed me down on responding to your posting: I was testing to make sure that my instructions actually worked, and (1) the client box I was using actually has an explicit "wireless on" and "wireless off" toggle that I forgot to toggle, and (2) because I changed my router to one that supports wireless, I had two machines that ended up using the same ip number since the new router automatically started at the same number as the old router when handing out DHCP leases. Neither will probably affect your setup, but passed along for what it is worth.)
Appreciated. It seems that for the card to work, a driver called either: BCMWL5; lsbcmnds; or WPC300N_20061107.EXE has to be loaded, but those options aren’t available. (The card is called WPC300N v1). Also haven’t been able to get Puppy to stay on the hard drive on even this computer (which works and with which Windows can be accessed—on Windows now; even on this computer Puppy hasn’t been able to be set up to connect to the internet).