Car Question: headlights don't work

I know there are some mechanical types here on the board and I hope this is an easy one…

1991 Toyota Camry LE 4dr 4cyl auto w/ A/C

A while back the car just died and I put in a new battery which eventually died as well. So I put in a new alternator and now it is running great. Everything works except the headlights. I have checked all the fuses and they are fine; the bulbs in the lights are fine as well. I suspect it might be the relay switch but I don’t know how to test it. The auto parts place says I have to test it myself with a volt meter but I’m not sure how to do this. Is the relay the problem or should I look elsewhere?

Are you sure the bulbs are good?
Do the high beams work?
Do the parking lights / tail lights work?
Can you flash the high beams with the headlights off using the high beam switch?
Are you sure, you’re sure the bulbs are good?

Double check the bulbs, are you sure there good?
Check the voltage at the socket, that should answer some of your questions.

All lights except headlights work. All electrical works. No high beams and I can’t do the flash of the lights either. I’ve just double checked the bulbs. They are fine near as I can tell. Filaments are there and not burned.

That is what I’m not sure about. I can get access to a voltmeter but not sure how to actually do the test.

Set it to 12v DC (or whatever the lowest DC setting you can set it to above 12v), pull out the bulb, put the red wire in one side of the socket, touch the black lead to a piece of unpainted metal on the car (find a bolt or something under the hood). Turn on the headlights and see if the meter moves, check the brights as well. If not check the other leads in the socket, one at a time. If none of them do anything, it’s the car, if they do make the meter move it’s the bulb.
Does that make sense? For some reason when I try to write this it always sounds so convaluted, it’s really very simple and should take about 5 minutes, including removal of the headlight.

ETA, you might want two people for this, it would be easier if one person can work the voltmeter and the other can turn the lights on and off. The other option would be to turn the lights on, then with the black wire grounded, check all the leads in the socket to see if any of them have juice. But that might cause some sparking.

Plug the red lead into the spot on the meter that says V-ohms and the blac lead into the spot marked common.
Set the meter to read DC voltage. (It may be a symbol that looks like a straight line over a dashed line)
Pu the black on the battery negative lead, and the red on the battery positive lead. You should read between 12.5 and 15V depending on if the car is running etc. If you get this reading proceed, if you did not get this reading, your meter is set wrong, find out what is wrong and fix it.
On the back of your light bulbs there are either two wires or three (depending on the headlight system)
On a two wire system with the light on, one wire has power the other is a ground.
I would note that on a quad headlight car the high beams only have power when the high beams are on. Low beams are the outer bulbs.
On a three wire bulb one wire is low beam, the other high beam, the third is ground.
OK to test:
Turn on the ign key. Turn on the headlight switch
Connect (hold) the black meter lead to the battery neg.
Touch the red lead to the 2 or 3 terminals at the rear of the headlamp. (One at a time) If the meter indicates no voltage, the circuit is dead. If you can’t access the leads due to the connector, unplug it and test the harness connector (not the back of the bulb), be gentle and don’t push the test lead into the connector and distort it, or you will be sorry.
If however one lead indicates voltage, then move the black lead from the battery and touch it to the other lead(s) (again one at a time) If the meter indicates voltage you have a bad bulb. If the meter indicates no voltage, you have a bad ground.
Beyond this it can get a little hairy fault tracing electrical systems over the internet with someone that has no experience.

I am no professional, But I would not use a volt meter to test as the other 2 suggest

I would use a 12 volt test light . A meter may show 12 volts present, but there may not be enough current to light a bulb. I have learned to use a light for such tests(the hard way).

If there is another relay which is identical to the headlight relay, switch them and see if the lights start working.

On the list of main suspects are a 40 amp fuse (one of those big ones, in the fusible link box near the battery), the headlight switch, and the headlight relay. The simplest place to test all of these is at the relay terminals. Two of those terminals should be hot (12 volts) at all times (if not, bad 40 amp fuse). One of them should go to ground when the headlight switch is activated (if not, bad switch). When power is applied to the remaining one, the headlights should come on (if not, bad bulbs or bad switch). If all the above check out, bad relay.

I hope the OP hasn’t been driving for 10 years with no headlights.