How do I know if I need a starter or alternator? 99 dakota 4x4 and when I turn key it clicks without turning over

With head light on, when you turn the key, do the lights dim out, if not then battery is ok, what you need to check is voltage at the startert assembly, with test light check voltage at big wire at starter, should always have voltage there, now on small wire should have voltage there only while key is in the start position, if you have voltage there, check voltage at big wire again, just to make sure you did not loose voltage there, if you did check battery terminals, if you did not loose voltage, bad starter, also after you have check voltage there and all check out good, get a hammer and hit the starter with key at start, some time it will start, if it does you will still need to replace the starter.

The problem may not be either. The first thing to do is to make sure your battery is fully charged, if the battery is fully charged then you have either a bad connection or a bad starter.
If the battery is not fully charged the next thing to do is to get the battery fully charged and have it load tested to see if you have a bad battery. Most auto parts stores will do this test for free.
If the battery checks out then your problem is most likely the alternator but before you just replace it have it tested too. You could still be looking a just a bad connection.
One thing that often gets over looked is a weak or bad grounding connection.