Linksys WRT54G router as a repeater in an existing LAN

This is yet another chapter of my home networking experience. It has taken me some time to figure out this (fairly simple) procedure. So I'm summarizing it here in case someone else intends to do the same thing, namely to add another router to your existing home LAN, e.g. due to the lack of free ports (on your existing routers) or as you want the additional router to cover areas that are currently not covered by the existing WLAN. So, this is what you need to do:

1. Most important thing: link the router up not via the WAN port but via one of the LAN ports.
2. Disable DHCP on that router.
3. Set the WRT54G to router mode instead of gateway.

By the way: I believe that this works similarly with other routers and is thus not restricted to this Linksys model.