How can I tell if my alternator is charging the battery?

With a DMM (Digital Multi-Meter) measure the DC voltage at the battery terminals while the engine is running. You should see a nominal voltage of 14.3v.

If you're having issues, check your battery as well. They usually have a lifespan of 2-3 years and have a tendency to die in cold weather and the stock batteries are notoriously weak. Consider replacing your stock battery with an Optima Gel battery if you off-road.