If there is a jack on an adjoining wall (I know you said adjoining ROOM), you can simply cut or drill a hole directly behind the current jack into the other side. That assumes the location in the new room is acceptable. Otherwise, you'll have to find a path through wall/attic or crawl space/wall.
You can buy a jack at almost any hardware store, Radio Shak, even Kmart. The same for telephone wire. There are different styles of jack. Most any will work and some don't require that you make a big hole in the wall.
Make sure the jack you buy has the connectors marked "red, black, yellow, green". That tells you where to put the wires. Simply connect the red wire from the red connector in the old phone jack to the connector marked "red" on the new jack. Do the same for black. Green and yellow are for a second phone line, but you should hook them up as well.

Last details: If the phone you plan to use is the old fashion non-modular variety, you'll need that type connector.
Finally, if you get finished and it doesn't work, make sure the old jack has the wires in the right place (red to red, etc.) I have seen some people mix up the wire colors.

OOPS, I think I made a mistake when I said green and yellow are for the 2nd line. My memory is fuzzy on which 2 wires are paired. Either way, connect all 4 wires and you'll be safe.

telephone wiring comes in several types. for jack to jack wiring use the solid conductor type. This is easier to use and connect under the screw posts. btw, the black and yellow are for the second line. There is also a 3 and 4 pair inside wall wiring. the colors that match there are the (1)blue-blue/white (2)orange-orange/white(3) green-green/white and (4) brown-brown/white. for better data transmission, use the type called cat 5. This is twisted more frequently and keeps possible interference from other line useage.