Hi There,
There is a way to do that ; it's called "peer-to-peer networking".
You will need a USB wireless access point (WAP) for each computer.
You install the "WAP" into each computer then you choose the computer with the internet connection to be the "Host computer" and set up a peer-to-peer network on it.
The network wizard will 'walk you through' the set-up and allow you to load the network settings on a flash drive which you run on the other computer.
After running the setup on the second computer; plug the flash drive back into the host computer and complete the setup
After doing that both computers have to be rebooted to set-up the registry properly. That is an important step in the process.
I suggest searching your computer's "Help and Support" for "peer to peer networking for a step by step procedure. Print it out or write it down for reference while setting up your network. Be sure and check "allow internet sharing" on the host computer. You also can select "file and printer sharing" also if you have the need.
My suggestion would be to just buy a wireless g router for the first computer and a USB wireless access point for your second computer. That is much easier to set up, more secure and only about $20- more cost. I had three computers on a peer to peer and although it works every week ot two I would have to set it up all over again. Since getting a wireless router have had no more trouble.
The router does exactly what it was designed to do ( work better than a peer to peer network).
Hope this helps, (get the router and a USB wireless access point)
Al