On live conductors, use only the AC Voltage function. Choose a range of 240 volts or higher. For your level of experience, this is the advice I offer.
Others will no doubt soon offer different advice.

You can use the voltage setting to tell if wires are hot.

You need a known good ground for the readings to mean anything.

If you do not know how to identify a ground to measure against stay out of the boxes.

Ground vs neutral? If they're bonded, what's the difference?

OP, you should pick up something like Home Depot's "Wiring 1-2-3" and have a good read, plus whatever you can find online before you start messing with it.

You need to know the basics, especially which wires you're connecting to to test, before you touch anything.

MOST importantly, when you do start playing around, label the wires and make a note of how they're connected before you mess with it. It'll save you a lot of grief.

"Ground vs neutral? If they're bonded, what's the difference? "

One is a current carrying part of the circuit and one is not.

I have a step by step home wiring guide book. I also got a Non-Contact Voltage Tester. Did not know they existed. Very handy.

The non-contact tester is very useful in some situations. But it often gives false readings. I have experienced both false negatives and false positives. It would not be my choice for the situation you describe.
For your test, a 40 watt lamp ("bulb") in a pigtail socket would work very well.

Plenty of videos on YouTube that show the use of a voltmeter.

For 120v circuits: hot to neutral or hot to ground should give you 120v. But the path back may be open so you should test hot to ground AND hot to neutral. Depending on my suspicion level and what I was trying to determine, I might use a non-contact tester or go from hot to a known good ground.

For 240v circuits: hot to hot should give you 240v. Either hot to ground (or neutral if present) should give you 120v. If you're testing a 240v circuit, testing hot to hot, hot to ground, hot to neutral (if present) would give you additional information about the integrity of the circuit.

I've never had a false negative with a non-contact tester, assuming the thing is working and used properly . Test it on a known live wire before use. False positives, yes.

"For 120v circuits: hot to neutral or hot to ground should give you 120v. But the path back may be open so you should test hot to ground AND hot to neutral. "

And when you find an open on both you wil lfind out when you touch a hot.

Use a KNOW good GROUND to test against.

Even if you have to use an extension cord to get from a grounded receptacle that you KNOW is solidly grounded.

It is not usually the 120 V that gets you, but the fall from the ladder you are standing on working on the light.

I actually have a retractable wire spool dedicated to going all the way the the panel.

Non-contact testers are not much more than a toy when you are considering touching wires.

Ok. I was wondering why you were talking about testing hot to ground.

"I was wondering why you were talking about testing hot to ground."

How do you test that a circuit is actually OFF?

Touch it and hope?

Use a KNOW good GROUND to test against.

I think that's what I said in the next sentence.

Under most circumstances hot to ground and hot to neutral is probably sufficient to determine if a wire is live. If the wiring job looked like a charlie foxtrot, then I might be looking for a good ground.

But you're right, it's falling off the ladder that will likely do the damage.

Umm, hot to neutral? Working properly, that's what a circuit normally does, right?

I don't know if testing hot to ground is better with digital meters, I really think analogue is more reliable in these sorts of situations - the phantom voltage you get with digital really can make you wonder if it's live or not.

"Umm, hot to neutral? Working properly, that's what a circuit normally does, right? "

That does not mean it is off or safe to touch.