Yes, the wireless Linksys router works with a PowerBook + Airport Extreme.
The router talks to your ISP (the WAN, wide-area network) and to your Powerbook (the LAN, local-area network).
To get started doing the setup, you'll use a web browser to talk to the router at a fixed IP address, e.g., http://192.168.1.1, and follow the Linksys manual for the router setup. The router needs to know both the WAN setup and the LAN setup you want.
For the WAN, you need information your ISP should give you. Most likely, they'll say to use DHCP (Dynamic Host Configuration Protocol), i.e., the router will be assigned its address by their server.
For the LAN, you can set up the router so that your PowerBook has either a fixed IP address or is assigned a dynamic address by the router, again using DHCP. In either case, you'll set the PowerBook to match by picking the right choice in the Network pane in System Preferences. For example, if the router is going to give you a dynamic address, you'd pick DHCP from the Configure drop-down menu.
I hope this helps. Reading this back, I'm afraid I made it sound too confusing.