Easy. You don't. Routers don't need installation at all. Just plug 'em into the modem. If you need to access any preferences for the router, simply type the following into your browser:
http://192.168.1.1I think this differs depending on your location or type of router, but I've owned many different brands of routers and this has always been the address I've used to get into the router's control panel. From the control panel you can add WEP encryption, open and close ports, and some even have the ability to change your MAC address (this is VERY useful for hacking). I've never installed a router in my life because it's not needed. If you can't connect at all, try unplugging the modem and router and plugging them back in about a minute later (modem first). Or you can try resetting the modem itself by using a paper clip on the back.
I've never heard of a wireless connection dropping because there was another wireless connection to the router. Could be a setting though. Go to your routers control panel (type in 192.168.1.1 or whatever number it says in your router manufacturers manual) and reset everything to default. If that doesn't work, I'd exchange the router.
