To extend your wireless connectivity throughout your home you do not need to hook an access point to the computer(s), just to the router. Buy a RJ45 cable at the proper length and plug one end into the Lan/Wan or uplink port of the main router or combination modem/router and plug the other end into the access point or range extender. Then at the point you wish to place the access point or range extender plug it into an available power outlet.
Make sure that there is little interference and good antennas on both units. Don't place near concrete, anything metal, and keep it away from kitchen appliances. It is also important to use a different range than your cordless telephone system. For example, if you use a 2.4 Hrtz phone buy a higher range on the wireless devices.
You may also want to download and install any device driver updates for your wireless adapters and install any firmware updates for your modem, router, or modem/router in order to keep all in good working condition. Make sure the wireless adapters antennas are pointed towards the access point or ranger extender if possible.