You'll want to load whichever module supports your adapter, that usually requires finding out what chipset the adapter uses, then find out which module, if any, supports that chipset.

Included modules are:
catc
dm9601
kaweth
mcs7830
pegasus

Extract from the .tgz like this:
tar -xzf usbnet.tgz

Load appropriate module, ex:
insmod mcs7830.ko

Then configure your adapter manually or via DHCP, and enjoy using command line utilities and other apps that don't try to bring up a connection dialog

No luck getting the browser to work, and no answer to my enhancement request on bugs.maemo.org, I haven't messed around with it for a while, was really hoping someone else would figure it out

Easiest way to make the USB connection would be USB-A-Female to Mini-B-Male for the N800, but for the N810 I'm not sure.

If all you want to use are "normal" applications, I don't think I'd bother getting an ethernet adapter until someone figures out how to make them see the connection, but if you want to just mess around, or use commandline apps, etc. go for it!