for wiring a car, you can almost get away with just a simple test light. Runs off 12v and it you have power to it, it comes on.
To use one, you just hook the clip to a common ground and start probing wires to see if they are hot (light on) or not.
A multimeter is pretty easy to use. While some of the more expensive ones will automatically switch to whatever you are detecting, its not mandatory.
Ok...so you can test for voltage...thats basically power. Set the multimeter for "DC" (Direct current voltage) and you need to select a range. You want the max voltage to be that number. We know cars use a 12v system, though you may see close to 14v from the alternator. So you would want to select the 20 volt setting. Its always best to start high if you dont know. You dont want to be on 1volt and pass 200 through it. Start high and move down. Basically voltage will be spit back at you in a number. This is one way to test if a wire is good or getting power. Same can be done with a test light. Attach the black (ground) lead to a common ground and the red to a source. If you see voltage, you its a hot wire.
Another thing to test for is ohms. This is resistance. So with your multimeter you select ohms. It might look like a goofy upside down "U". With this, you put one lead on one side of the wire, and the other lead on the other side. This give you a numerical display of the resistance of the wire. When sending power down a wire, you always lose some of the juice. To compare, you are pouring a qt of oil down a funnel...not 100% of that oil will make it out of the bottle and through the funnel...you will lose some. Same happens with electricity. Usually the thicker the wire, the less loss. The electricity flows over the surface area of the wire, not the center. This is why you will see "MONSTER cable" for home theater. Its not the diameter thats important...its the surface are of the conducting wire.
Amperage is also something you will run into on a car. If you look at a battery, the battery will show its amperage. The easiest way to describe amperage is the amount of balls it has

How can we compare this to an engine.... Say a 302 has 300hp... the hp could be compared to amperage. You can have another 302 that cranks out 400hp. The motor is the same size (voltage) but the 2nd one has more power. So again, back to using your multimeter. You can check for amperage by selecting it on the meter. Then you connect to a hot and ground source. It will spit out a number. A car battery is a good source IF your meter will support readings and has the capability of reading over 400amps. This can fry your meter. Just like the motor comparison...a stock 302 motor isnt going to hold 1000hp...its gonna die. you will use this setting to test an alternator. A stock alternator should put out 60-80amps. If you are putting out less, its not able to fully charge the battery and run the electrical system of the car.
The other main option you will see is AC voltage. That is alternating current voltage. With AC voltage, typically you will have higher amperage ratings. AC voltage is electricity is the electricity in your house. Same stuff applies with detecting DC voltage and amperage. I dont suggest EVER trying to read amperage in a house with cheap multimeter. Your typical house circuit will will have 20-30 amps max capability and that is determined by the circuit breaker. The main power to your house is HUNDREDS of amps at 110+ volts.