Assuming that you use some kind of broadband service (ADSL, Cable) via a suitable modem the answer is yes but .....
You connect one as usual, connect the other one to it via an Ethernet cross-over cable and then set up Connection Sharing in Widows.
The but is this can be difficult to do if you are novice and the computer connected to the modem has to be switch on for the other to be able to connect to the internet.
My advice is to buy a router. It will be much quicker and easier to set up and they can be got very cheaply these days.
t
April 2008