First, don't install the software that comes with the router. This is very important.
Simply power up the wireless router. Once powered up, search for the default name for the router in the list of wireless connections. For Linksys, the network is named Linksys by default. You can change this later.
Once connected to the router, you will be assigned an IP address. From the cmd window (Windows->Run->CMD), enter ipconfig. You should see the IP address as 192.168.1.101 (at least this is what Linksys starts with. The gateway listed below is the address for your wireless router.
To connect to the wireless router, you can now enter the "gateway" address as described above into a browser window. Keep in mind that if you change the name of the wireless network name, it will disconnect your laptop from the network. This is ok. Just find the new name in the available networks and reconnect.
Other laptops can connect too. They will be assigned a new IP address after they connect.
For some reason, tech support for Linksys believed that an Internet connection was needed for their wireless router. They are clueless. Follow these instructions and you'll have your wireless LAN up and running in no time.