First, go to the web configuration page. This is usually located at http://192.168.1.1/ log in as the administrator, i'm not sure what the default password is for the wgu624 is. Most routers the username/password default is admin/admin. Hopefully you actually changed this during install :) Then from the main menu, go to Maintenance, then Router Upgrade. Then you should see a Browse button so you can upload the .bin file you downloaded. It's really important that the router is not powered down or disturbed in any way during the next few minutes while the new firmware is installed.
On the same screen that you upload the new version of the firmware, there is an option that the router can check automatically for new versions. This is handy, but if everything is working fine, there isn't any reason to upgrade.