Getting your Windows 3.x computer on the internet can be a lot of fun, so here's a little guide to help you to get online.
For this to work you'll need to install Windows For Workgroups 3.11 as the TCP stack can only be installed in that version.
In terms of hardware, I would say that the easiest option is to go with a wired ethernet card.
My recommendation for this is a PCI network card with a Realtek RTL8139 as it's easy to find and it's super easy to get working not only on Windows 3.x but in most other operating systems.
You can find the drivers for this one right here.
You're not limited to this network card though, especially if you need to use an ISA card, there are plenty of other ones that work fine with Windows 3.x.
Another option is to have a dial up modem and setup a dial-up connection with an ATA device.
This is a fun but more complicated way of getting your Windows 3.x PC online and I'll add more information on how to go this route eventually as I'm working this out myself at the moment.
Regardless of what route you go, you'll need drivers to use the hardware you chose to get online.
As I mentioned before, you can get the drivers for the RTL8139 here and I'll eventually add more networking drivers there.
If the driver you're looking for isn't available there, a good place to start looking them is the VOGONS Vintage Driver Library.
I'll add a guide on how to install the drivers soon:
Unlike Windows 95 and newer versions of Windows, Windows 3.x doesn't come with the TCP/IP stack installed by default, you have to install it yourself.
The TCP/IP stack is what allows your computer to have an IP address assigned to it so it can communicate with other computers on your network and also to make requests to websites using HTTP.
Sadly, as I mentioned before, Windows For Workgroups 3.11 is the only only one in the Windows 3.x family that can have the TCP/IP stack installed.
You can get the TCP/IP right here.
I'll add a guide on how to install it soon, but it should be pretty straightforward.