Looking for or adding a ground to an existing NEMA 10-30 socket
A ground wire in a NM run for a dryer is indeed an unused fourth wire in the box, and it will be bare.  If your garage dryer socket was instead run using AC (BX, in other words) or metal conduit, then the box itself is grounded, and should be pigtailed to to ground the receptacle.  (In the rare case the circuit was run with MC, there will be a green ground wire in the box.)

If you're comfortable using a multimeter, you can turn the circuit off at the panel and measure the resistance to the neutral wire -- the ground will only have a few ohms to the neutral as they are connected at the service entrance.

Adding a ground to a three-wire, 120/240VAC circuit is best handled by running a separate ground wire back to an allowable grounding point as per NEC 250.130(C), using single conductor bare armored ground cable.  In the 2014 NEC, point 4 does allow you to tap the nearest EGC of a suitable size originating from the same enclosure as the recipient branch circuit; but, since a 30A circuit needs a 10AWG copper EGC, you can't use a 15 or 20A circuit's EGC as the donor.

Also, if your appliance can do it, you can install a neutral bonding jumper and change it over to a NEMA 10-30 plug on a 3 wire cord. (Just about all dryers can do this.)