You can look at the wire, either coming out of the breaker (you will probably have to remove the front cover of the panel) or at an outlet. The wire may be marked with the gauge of the wire. If it is, it would probably be easier to read at the panel, since the wires at the outlets are usually coated in drywall mud and paint.
It it isn't marked, you will need to measure the wire itself, either with a gauges, or maybe with wire strippers that are marked, or comparing to a known wire.
All of this should be done with the power turned off (at the breaker when working at the outlet, at the mains if messing with the panel).