My left headlight on my 1990 chrysler New Yorker doesn't work, Unless I have my brights on than they all work

assuming that the bulbs are good, then check the connector itself. also, unplug it and see if you have 12 volts or so at the connector.

How can I check to see if the bulb is any good I unplugged it and took it out but the case around the bulb won't open up? How do I get the bulb out

You can usually tell if a bulb is bad. It will be dark inside. Sounds like it is your low beam bulb that is out. Check for 12 volts at that connector while you have the low beams on and if there is voltage then replace the bulb.

How can I replace the bulb if it is stuck Inside of this

Of it's container

I know I might sound pretty dumb but I'm still a little bit new to this but how do I check for voltage at the connector I don't really understand that

You will need a test light or multi meter to test for voltage. A little cheap test light will work. Turn the lights on , ground the wire end of the tester to something on the engine and stick the probe in the connector. If it lights up there is power and the wiring is ok. then you know it is the bulb. On your vehicle you may have to replace the whole headlight, on some models the bulb doesn't come out. If it does, you should be able to twist the bulb and pull it out. Btw, there are no dumb questions.

A cheap test light looks like a screwdriver with a point on the end and a clear handle with a bulb in it. It will have a wire coming out the handle end. Just a few bucks, good thing to have in your tool box!