Hello,
While I don't like seeing workstation-class machines working as servers, I can understand for cost / business reasons what you are trying to do, and think we can get something working well for you concerning it.
My knowledge of Win 3.1 is a little thin, but I think we can hammer this out. You will need a network card for it, and will need to install NetBIOS / NetBUI protocol on it. Windows 3.1 did not come with a free IP stack... but if you can find TCP/IP for it, all the better. You are looking for something called WinSock, and it might be available to download from somewhere. I think you will need an ISA ethernet card, and will need the driver floppy disks for it. Be sure to blow the dust out of that floppy drive if you have not used it in a while.
You will also need a network hub, and wiring to connect the two computers to the hub. Do not use a crossover cable from one computer to the other computer. That seriously limits growth potential later on.
On the Windows XP machine, you will need an ethernet card to go to the hub. If this computer also goes to the internet, you will actually need 2 cards, or you will need to change what was described above so that they go into a router instead of a dumb hub/switch. If you need Internet capability, you can purchase a router, and from there add your XP and 3.1 machines to it. I'll wait for your reply before we go any further.
From there, you need to create a username / password on the XP computer for the 3.1 system to use. You also need to setup file sharing, and have proper permissions. You also need to make sure the NetBIOS / IP system is properly configured.
If you get TCP/IP working, grab a copy of VNC. It is free, and it is remote-control software. Install the server on the 3.1 machine, and the viewer on your XP machine. Set a password on the server. Set it to also re-launch if the 3.1 machine is rebooted. You will now have a remote-control solution, and won't need that monitor back.
Finally, have the 3.1 box login to your XP box, and share files back and forth. You will need to initiate that connection from your 3.1 box, either using a monitor, or the VNC software. Also realize that you will probably want to keep the XP machine on full time now, and that you should put UPS backup power on each box to minimize "maintanance" on them. You might also be able to get the 3.1 box to save everything on the XP box, so that you don't need VNC so much.
I know this was high-level and not step by step. If you need that, let's talk.
Christian