Wire size of unmarked wires
There should be markings on the cable jacket. If you can't read it due to age, measure the thickness of the wires with a caliper, or a pair of wire strippers. Modern NM cables are color coded, but older cable was not. So jacket color means nothing with older cable.

Checking the size of the breaker could give you a clue, but only if the cable was installed properly. If wired properly, 12 AWG should be used on a 20 amp circuit, while 14 AWG is good for 15 amp circuits.  

14 AWG wires are fairly easy to bend, while 12 AWG are a bit stiffer. Though this is only helpful, if you're familiar with working with wires.

If you had a piece of wire of a known size, you could use that to compare. Though you'll want to compare the metal part of the wire, as the insulation may be slightly different even on the same size wires.