That looks like at least 4 pair wire. The first line in a given dwelling unit is the blue/white(ring)(-) white/blue(tip)(+) pair. Obtain a modular jack which will mount to the box shown-failing that use a low voltage foldable plaster/drywall mount.
Attach the wires as identified above to the jack using the included plastic punchdown tool, or if screw terminals identified for quad cable (red/green/yellow/black), remember red=ring and green=tip.
If still confused, post again, and I'll try to confuse you further.
