Buy yourself a simple load tester, EVERYONE should have one. Put it on the battery and it should have a little over 12v, start the engine and it should go up to 13+v or so, rev the engine and it should go up to 14v or so. If everything is operating properly, this is how it will go. If your alternator/charging system is not working properly then the voltage will not increase when you start the engine. If it does go up, battery is the problem. Remember to check belt tension and battery terminals for tightness and that the connections are clean. You should not be able to twist the cable end connector by hand, if you can then it's too loose.
To test the battery, check voltage, disconnect it and trickle charge it overnight. Ck. voltage with the load tester and it should be 12v or more, load test it (should be a button on the tester) for 5-6 seconds and the voltage will drop and then come back up to 12v. If it does = battery good, if it does not = battery junk!