Most meters like yours work the same way. You can see from the legends printed on the front next to the jacks what you are going to measure. You plug the two test leads into the jacks.
One is "common" and is where you plug the black lead. The red lead plugs into the jack on the right. (It doesn't matter what color goes where, but that's the way you keep them straight in your mind while testing.)
Start learning by doing...plug the leads into the jacks, and turn the meter on to the Vac 200 position. It's in the red area at about the 1 o'clock position. That stands for "zero to 200 volts alternating current." Some meters have a scale that is lower, for instance 0-20, or 0-150. If you now turn on your train transformer, and it's connected to the track, you can touch one lead to an outer rail, and the other lead to the center rail. The meter should register the AC voltage that you are supplying to the track. Turn the transformer handle either way, and you will see the reading on the meter change.
To measure "continuity" you leave the leads plugged into the same two jacks, and turn the selector handle to the 200 ohm position, in the green area at about the 6 o'clock position. In this position, the internal battery is put in series with the leads and the meter. DO NOT USE THIS POSITION, OR ANY OTHER "OHMS" POSITION TO MEASURE VOLTS OR AMPS!
Take a known electrical conductor, such as a piece of track, wire, spoon, etc, and touch the two leads to the item. Or just touch the metal tips of the two leads together. The meter should register close to zero ohms. That means that there is very little resistance, which means electricity can pass through easily.
You can use the meter to monitor if a controller, or pushbutton, or track contactor is doing its job. Put the red lead on the switched wire, and the black lead on a common transformer connection, and watch the meter indication.
I wouldn't try opening a transformer and poking around with the meter leads until you are a little more experienced. But you can take the leads and use them on the various posts of a transformer and watch the Volts AC readings. You will gradually start to understand what's going on just by doing a few tests.
A continuity test is useful for hundreds of conditions on your railroad. It can determine that both rollers on a locomotive are wired correctly, or that a light bulb is not blown out, or that a piece of track is not shorted, etc. It is simply a way of showing that electrons are flowing though a circuit.
The Volts DC scales use the same jacks. Those positions (upper left quadrant of the selector) measure Direct Current, such as what comes out of a flashlight battery, a "wall wart" DC supply, your car's battery / alternator. etc.
Open the hood of your car, with the engine OFF, put the meter leads on the two battery terminals (red on + black on -) and take a reading. It should say 12 Volts, roughly. Now start the car, and do the test again. If your alternator is charging correctly, the meter should now say anywhere from 13.8 to 14.2 volts. See? You have just learned how to check a car's charging system.
The third (left) jack is hardly ever used. It's just for testing one range of current (amperage) up to 10 amps, which is a lot of current, such as what a train would draw as it runs around the track. It requires some more understanding of how electricity works. You need to understand the difference between a series connection and a parallel connection. Once you understand them, then using the amps scales will be easy.