Desktop or Tower?
Easiest way if you have a Subway would be USB Ethernet adapter. There is probably a list of a supported ones somewhere if you have a search.
Another option is 16bit PCMCIA Network Card, Wifi ones also work. You need one based on the Prism2 or CNET Chipset.
I asked about Tower/Desktop because if you have Towerd your A1200 you might also need an PCMCIA Angle Adapter to use the PCMCIA port.
You will also need a TCP/IP Stack, OS3.9 has Genesis however I use MiamiDX as I find it easier to setup

There are lots of supported PCMCIA cards but the one I use is the NetGear MA401.
If you want to surf the Internet the two main browsers are IBrowse and AWeb, both functional but not great by todays standards for modern Websites.
Steve.