Like most routers, the LinkSys I believe you're interested in has a configuration system that is accessible by web browser.
You'll want to enable Network Address Translation - NAT - on your router. When the router is operating in NAT mode, it creates a private local network that masquerades as a single computer when identifying itself with your ISP's systems. With NAT, the router consolidates your network traffic when sending it out and distributes it to the appropriate computer on your local network when receiving it.
When you are using NAT, your computers will have private IP addresses that are only meaningful to other computers on your local network. These private IP addresses can either be assigned manually or dynamically, using DHCP. Since this isn't a wireless setup, there is no security risk in choosing DHCP, which is probably the simplest way to go.
The router itself will be easy to configure. The little web-based interfaces, coupled with the manual, are easy to figure out. Just turn on NAT and DHCP on the router according to the manufacturer's instructions. In System Preferences>Network on both of your machines, just specify a DHCP configuration of your Ethernet connection.
Good luck and don't worry.
Peter