You can leave the other cable connected or not, you are merely concerned with the router's wireless section.
For setup, really you should consult the router manual (usually a simple download from the maker's site) or the quickstart leaflet which usually comes in the carton the router was delivered in.
Briefly, you need the address of the router, usually 192.168.0.1 or 192.168. 1.1 and put that into the address bar of your browser. You should be greeted by a login box and must supply a User Name (usually admin) and Password (usually password).
Once in go to wireless check that wireless is enabled and either read or reset the wireless security WPA-PSK TKIP passphrase, save setting, log out.
Disconnect ethernet, apply new passphrase to wireless adapter setup and see if you can connect.
If you can't connect, repeat above but turn off wireless security. Also check that Access List, include by MAC ID is switched off.
If that solves the problem, you have a clue that wireless security is the problem.