You also need to make sure the two distinct local networks aren’t using the same address space, otherwise the router between them will be unable to properly route packets. If his router is set up to use 192.168.1.x, for example, you should make sure yours isn’t (i.e. manually configure it to use 192.168.2.x).
One issue you’ll run into is that if your router performs NAT, his computer won’t be able to initiate a connection to yours, and you’ll probably have problems doing things like filesharing and game-playing unless you know what you’re doing to configure your router to let this traffic “in” (since in your proposed configuration, his network is “the internet” as far as your router is concerned). If you just want to get on the network and browse the web, check your email, etc, you’ll be fine.
The “correct” way to do this is to put your linksys router in “bridge” mode, which means it connects its wireless network to your friend’s LAN, but ceases to operate as a router. This decreases the difficulty of setup, too, since it removes IP addressing as a variable – you just end up using the addressing scheme that the existing network has.