Wireless for igorant people?

First... I am computer fallible. Basically I can turn the dam thing on
and that is about it. I am however smart enough to follow basic
directions if I understand the language. After reading most of these
posts I realize that you are all talking a different language than I am
used to.

The Question Is:

I have a computer that has a DSL connection through a wire to an
ACTIONTEC wireless capable modem. I use my laptop to connect to this
regularly and want to keep it this way. I have fairly good reception
(exc to good) throughout the house.

I have a second computer that we got from SANTA this year for the kids.
I have set it up in a position of the house that we get better
reception. I have an older, (1 to 2 year old) LINKSYS WRK54G wireless
4 port broadband router.

Can I use the LINKSYS to be a receiver for the signal from the
ACTIONTEC to be sent through wire to the new computer, or do I have to
buy a receiver.

Any HELP in non-computereez would be greatly appreciated.

TERRY