The situation:

You have and existing Internet setup consisting of a single computer connected to a DSL modem.  The handoff from the modem is an Ethernet connection using Point to Point Protocol over Ethernet (PPPoE.)  The computer contains the software that logs onto the Internet.

You have a second computer that you wish to also connect to the Internet.

The Solution:

A Cable/DSL router and a couple of cat-5 patch cables (which may come with the router!)

Connect one of the several LAN ports of the router to the second computer.  The default on the computer should be DHCP, which will accept an IP address from the router.   Run Internet Explorer, point it to the router's webpage (see router manual for address of the router.) 

Continuing:

In the appropriate places set the router to use your name and password that you use to log onto your ISP.  Pull the ethernet cable off the first computer and place into the WAN jack of the router.  It should connect to the Internet and you should be able to surf the web.

 

Finish:

Connect your first computer to another of the LAN ports on the router.  It too should accept an IP address from the router and should also be able to surf the web.

As a bonus, if you share a directory on either computer, the other should be able to see it -- basically making that directory a part of itself.