You asked at the right time, I have literally just managed this very same task.
You will need:
1) A copy of AmiTCP (or another TCP/IP stack).
2) A PCMCIA network card. I'll upload a picture of the one I am using presently, it was a cheap ebay job.
PCMCIA NIC:
See here3) A copy of cnet.device, available from aminet.
4) CardReset, also from aminet. You might not need it, but it is useful.
5) A router - hopefully if you have a network connection from an existing PC you'll already have one.
6) A Swede*
Plug the network card into your PCMCIA slot and connect it to your router. The link light should come on when the A1200 has power, or at least it did on mine.
Assuming you are using AmiTCP
Install AmiTCP and when it asks you what sort of network adaptor you are using, lie and say an CBM A2065 board.
When it asks for your IP address, give it a suitable one from the range your router allocates. In my case this was 192.168.0.4 since .1 is the router, .2 my PC and .3 the A1XE. When it asks for the default gateway, use the address of your router. Same for Name Server.
After installation (before rebooting), put the cnet.device (020 or turboio) into sys:devs/networks.
Edit the db/interfaces file in amitcp's directory and change the 2 occurences of a2065.device to cnet.device
Edit the db/hosts file in amitcp's directory and add your chosen IP address with a hostname underneath the localhost entry. Doesn't matter what you use for a hostname as long as it is legal. a1200.w00t.net or something equally triumphant should do

Reboot.
If all has gone well, amitcp will start at boot time and you will have connectivity. You can test this by opening a shell and pinging your router. Or open a browser, if you have one installed.
If you do have problems, try using the CardReset command in your user startup before any reference to amitcp. Your machine might fail to assert the _RESET signal on the PCMCIA when the machine reboots. CardReset addresses this issue.
If you have a towerized A1200, think about how much room there is between your PCMCIA slot and the tower casing. You might need an L-shaped adaptor. I got lucky, but only just:
See here*If all else fails, talk to your assigned Swede via IM, who will patiently get you through the whole process. It worked for me, YMMV :-)