Here's where I get to contradict two people in one post. I personally had the Eiger 10BT card, but never got it to work under Windows 3.11. Gave up after way too much time spent on it. On the other hand, I have a Xircom CE-II-PS and I'm really happy with it. It comes with NDIS3 drivers, a graphical installer... and it works pretty much out of the box. The DOS packet drivers were equally easy. Just launch the packet driver loader, that's it!
Early PCMCIA implementations varied, and getting PCMCIA anything working on DOS or 3.1 can be fussy. Windows 95 had its own built-in card services that mostly worked automagically, whereas earlier systems relied on a combination of PCMCIA card services suites and PCMCIA hardware providing its own bare iron drivers for the various PCMCIA controllers. I've never been able to get 16-bit card services to actually work with a card -- it requires lots of manual configuration for each card, and uses lots of conventional RAM.
The network drivers, as others have said, will still require you allot them a free upper memory space. Chances are good the default WILL conflict with something and the driver will just freeze instead of gracefully reporting the conflict. And yes, MSD is your friend. Can't do PCMCIA 16-bit without a memory snoop utility.
I'm guessing many early PCMCIA adopters just called tech support and had them guide them through every step.