Extend Wireless By Adding Extra Router Via Ethernet Wall Port?

My dorms have wifi in the common room, and ethernet wall ports in the rooms since wifi doesnt reach that far. They both have the same network name (e.g. the wifi network is named 'apple', and when i connect through ethernet in my room the name is also 'apple') I need to have wifi in my room. So, if i get a router and connect it to the ethernet port in my room's wall, would that work? Is that all you have to do or is there some other stuff i should know about?also can i put a password on it? And also, will it carry the network traffic of the common room?(if two people are using the common room's wifi, will the wifi speed in my room be affected nd whatnot) i have a linksys router lying around at home (the blue one with the double antennas, everyones seen them, and the one in the common room is the same...wireless g)