First of all, you need some SCIENCE!
A multimeter measures one of three things: Current, Voltage, Resistance.
Current (I) is the flow of electricity (how much water goes over the falls) In a one path circuit, the current is a constant throughout (i.e. ALL the water reaches the bottom)
Voltage (V) shows how much potential energy the current is carrying. (How high the waterfall is).
In a single path circuit, the voltage drop is 100% (i.e. at the top of the waterfall, the water has a high gravitational potential. At the bottom, it has zero. -- All voltage is consumed throughout the circuit.)
Resistance (R) is the property that consumes the voltage. Think Rocks or shelves in the waterfall that stop the flow temporarily, reducing it's energy.
These three properties are related by Ohm's Law (V = IR) Although I prefer the rearranged form I = V/R, which lends itself to the idea that Current goes up with voltage, and down with resistance.
Now look at this: http://isaac.exploratorium.edu/~pauld/summer_institute/summer_day15current/ammeter.html
It's a quick experiment into the construction of an ammeter, which measures Amps (current). This is how the multimeter works.
In order to measure current, you need to set the probes into the AMP socket and the Common socket. Then you need to break the circuit, and connect the probes so that the electricity has only one path through the meter. Set the dial to your best guess at the range (usually there are ranges from microamps to about 10 amps). Power up the circuit and read.
In order to measure voltage you need to move the probe to the V/Omega connector. Then set the dial to the appropriate voltage range (20 volts for most DC electronics, 200 VAC for wall current and also note whether it's got a _ symbol or a ~ symbol (DC vs. AC). To probe a voltage drop across a circuit component, you need to put one probe before the component and one after. What's really happening inside is you are sticking a reasonable large resistor into the circuit, and measuring the current through that resistor and the ammeter. (We measure Current, we know the Resistance, and we calculate the voltage -- but the meter does this for you.) Since the resistor is so large, it usually won't affect the circuit, as we're only stealling a tiny bit of current.
To measure resistance, power off the circuit. Set the dial to the resistance settings (Omega) and put one probe on either side of the resistor. What's happening inside is that we've switched from passive mode to active mode. That is, the power for the circuit is now coming from the meter battery. We know this voltage, we measure the current and use R=V/I to calculate the resistance. (again the meter does this for us.)