Hooking up to a battery is an easy, quick, and dirty way to test an electric motor. The blower should have a plug with 4 prongs inside--one of these is ground, the other 3 are hot and set it to different speeds. If you supply 12 volts to the hot side and ground the ground side, the motor should turn.
BTW, most common "failure" of blower motors is they get gunked up, and friction keeps them from being able to turn. If you pull the motor out, soak the moving part with an electric-safe penetrating lubricant (such as WD-40) and work it back and forth a little to get the gunk out, you can usually get it to work again. I've revived 4 or 5 blower motors that way, lots cheaper than the junkyard.