Okay, first of all, you should really have a much stronger grasp of basic electronics before you attempt to use a multimeter. But if you insist on being John Wayne, here's a basic rundown.
The symbol that looks sort of like a horseshoe is the symbol for Ohms. Ohms is a mesure of resistance. All elecronics have a certain degree of resistance, and there are components called resistors. Too much resistance and no current can flow.
The symbol that looks like a dashed line next to a solid line is DC current. DC current usually comes either from a battery or is created from AC current using filters, rectifiers and transformers. DC current moves in one direction and is what is always used to power micro-electronics such as those inside an arcade cabinet.
AC current is symbolized by a little wiggly line that looks a lot like this:~ AC current is known as alternating current and it is what comes out of the plugs in your house. Alternating current changes direction, normal American house current reverses direction 60 times every second, referred to as 60Hz.
The capital A means Amperes. mA means milli-amps, which is one amp divided by 1000. An ampere is a measurement of current.
The arrow with a line in front of it is a setting on the multimeter that allows you to test a specific electronic component called a diode. A diode is a component that allows electricity to flow one way, but not another. LEDs are a type of diode, one that emits light as a product of its normal operation. If you attempt to hook an LED up backwards, no light will be produced.
The arrow that is made up of a bunch of lines and usually points downward is the symbol for ground.
The little symbol that looks kind of like it makes sound (and is usually right next to the diode test setting) is a continuity test. It will beep if two points are electrically connected.
Now, as for troubleshooting...
If you are troubleshooting, you have to know what you are looking for. For instance, if I were TSing a printed circuit board, and I was trying to find out if a component was getting a certain number of volts, I would have my meter set on DC current. If I was trying to find out if a machine was getting wall current, I would have my meter on AC current. (Just for the record, the likelihood of you trying to test for AC current is rare, and dangerous if you don't know what you are doing. 120V, 60Hz wall current can stop your heart. Easily.)
If I'm trying to find out if a resistor is bad or if there is too much resistance in a circuit, I would have my meter set for Ohms. If I am trying to determine if a wire run is cut or incomplete, I can use the continuity test between two points. I can also use continuity to trace a difficult to follow circuit or wire run.
Honestly, a Dummy's Guide To Multimeters is a little bit like a Dummy's Guide To Base Jumping. Yeah, if you read enough, you may know what people are talking about, but you're still taking your equipment and your life in your hands when you actually try to do it. My best advice to you would be to make friends with someone who is willing to actually train you on electronics and multimeters, someone you know face-to-face who can show you what to do and, more importantly, what NOT to do.
If you have any specific questions, please don't hesitate, no one wants you getting zapped because you thought you knew what you were doing.