On my thinkpad A31 wlan is detected automatically by lubuntu and debian (prism 2.5 support is part of the kernel, so no firmware is necessary), but with paldo stable (fresh install) no wlan connection is displayed.
What do I have to install to make my wlan adapter work?

"No wlan connection is displayed". Does it detect the card? Do you know what driver to look for? Perhaps try lsmod in your Debian install or live cd to see what module drives the card there. You may have to do some manual configuration if it has been dropped from the recent kernels.