I'm not going to step by step this, but basically it's like this...
One computer, we'll Call Computer A, has 2 ethernet cards, and another Computer, Computer B, has only one ethernet card.
If you don't have a hub, then you'll need to create an ethernet cross-over cable, and if you're not certain how to do that, then read this:
In a generic way you want your cable to be:
White-Orange - pin1
Orange - pin 2
White-Green -pin 3
Green - pin 6
(this is the normal ethernet side)
White-Green -pin 1
Green - pin 2
White-Orange - pin3
Orange - pin 6
(crossed - side)
If you're not making the cable yourself, then buy an Ethernet Crossover Cable.
Then you will connect the two together, giving B an IP that you define, and then the ethernet card you connect to B and IP that you define to be the other side.
Then route B to A by defining the Gateway to be A. Set up A's other ethernet interface to connect to the world as normal (DHCP or whatever) and, depending on the version of Linux you have, you may need to route the network from B to A on the A box.
But really... if you have a single internet connection, and you can afford to just buy a cheap switch for like $30, then do that and save yourself a shit ton of hassle. Plug both devices to your switch, and then let it take care of all the local stuff.
If you're using dial-up, and you only have modems... everything is different. It really sounds to me like you need to put a lot more detail in your question before someone technically adept can actually answer your question.
That's just me, though.