I've got 2 machines with WFW3.11 and TCP/IP.
First one is a 386/25 generic computer with a 3COM ISA network card, I used this card because the drivers are included with WFW. As you know you only get Netware and NetBEUI by default, so I added TCP/IP (with tcp32b.exe as advised) and removed the useless Netware. Works well enough.
2nd machine is a 500MHz Celeron, with a PnP Intel E100B PCI network card. Added TCP/IP just like the one above, works pretty well too.
I don't use DHCP here, everything has hard-coded IP addresses. I don't know if DHCP works with tcp32b.exe anyway.
Once you've got it running and can ping something, you could try installing Opera and see if you can connect to Google or some old http site. Opera isn't very stable and is also trialware, but at least you can test your internet connection with it.