Adding SMC AP to Linksys router - Help

I have a Linksys befw11s4 router which is several years old running
1.37.9b, Jun 21 2001, of the firmware. It connects out to a Toshiba
Cable modem, and then to Cox, my ISP. I run both wireless (3 laptops
and a desktop [dt]) and wired (3 to 5 dt's).
Someplace I recently read, but did not bookmark , about just adding
an AP to a router as a method to increase my "range".
I've also got a SMC 2655W AP v1.
I've tried hooking up the AP to the wired side of the router, through
a switch.
I was able to connect to the router and reset it's parameters.
I first reset the IP on the AP so the first 3 octals were the same -
192.168.1 as my home net. To do this I had to reset the dt I'm using
to control it to a fixed IP. At that time I then could not use the dt
to connect to the router, or the world.
I shut down, disconnected, reset the dt to DHCP and reconnected to the
router and the world.
I then went back and tried again (set dt to fixed, connect, etc), this
time resetting the SSID on the SP to linksys (as it is on the router).
At this step I lost connectivity to the world and had to unplug the
AP and do a hard reset on the router (push the button in the back).
Since I've from 2 to 4 users on at almost any time it's a pain to
experiment.

Any helpful suggestions on getting the AP to work ?