First step is find the room that has all the cables in it. If its it has phone jacks the ends of the wire in the common room are likely in a special phone patch panel.
The common way to solve this issue would be to replace the rj11 jacks with rj45 in the rooms. You would then remove the wires from whatever phone connection there is and put rj45 plugs on the end in the common room. You would plug these into a small switch. You should then be able to plug your router into a wall jack it go to the common room though the switch up to the other room.
There are other ways depending on how many jack you want active and where you router is located in relation to the common room.