Can I use the linksys WAP54G access point to make my wireless signal from my WRT54GS reach the 2nd floor?

You have the right idea. Before you go out and buy a 2nd access point, try moving the wireless router around, sometimes a couple feet left/right or up/down makes a difference. The average home has lots of multipath interference, sometimes because of things you cannot see like metal ductwork in the walls. The best bet it to have the wireless router as close to the center of your home as possible, but at least a few feet away from things that would cause interference like your PC chassis, metal filing cabinets, etc.

Also make sure that BOTH antennas are pointing straight up, despite how some of the pretty pictures look. This stuff all uses vertical polarization and antenna diversity so it’s best to have both antennas in the same orientation, both straight up.

You also want to make sure it’s not interference that is causing your lousy signal on the 2nd floor. It could be a neighbors WLAN running on the same or a nearby channel, or a 2.4GHz cordless telephone system, etc. It only takes a minute to try, so change channels on your WRT54GS and see if anything changes.

If you run twisted pair to the 2nd floor and place an ordinary WAP54G up there, you wouldn’t have the speedbooster benefits of course, but it should work just fine. Other (recommended) option is to get another WRT54GS, but just hook it up on the LAN side without using the WAN port. Then you have a more consistent home network and speedbooster capability throughout, which you should have if you invested in speedbooster cards for your laptops and PCs. You would also have the option of hooking in other wired devices upstairs in the future.

Whichever you choose, first hook up the 2nd device by itself and change it’s address to 192.168.1.2 for example, so you don’t end up with a duplicate 192.168.1.1 address with the first wireless router. Also, MAKE SURE that you select different channels on both of them, choose from the only 3 non-overlapping channels, 1, 6 and 11. Finally, make sure you set up identical security settings (WEP or WPA keys) on both access points. Then take a laptop and walk around, as you walk upstairs or downstairs (sometimes after several seconds) the laptop should roam between access points if you have set it up correctly.

When in doubt and if it’s not working, call Linksys tech support, they’re generally very good about helping out with this type of setup.

[Follow-up] Oh, and disregard kam_cute_bai’s answer, it is an exact copy and paste of mine. Thanks kam_cute_bai, I will take that as a compliment dude.