First I will echo what everyone else said, start by checking for loose wires. Especially ground wires.
With that meter, in order to measure Continuity turn the knob to the second setting (the omega sign, stands for ohms). Using that setting, you can measure how much resistance is present within a circuit. A reading of 0 means NO resistance and therefore perfect current flow. A high reading means high resistance, which impedes current flow.
For example, if you placed your leads on either side of a perfect wire, you would get a reading of 0. Meaning, there is perfect current flow through the wire. Now cut the wire in half. Your reading will jump to infinite or extremely high. This is because current cannot flow through the wire.
That is basically all you are doing with the meter. Placing the leads on either side of a circuit, and measuring the resistance. On most circuits, you are looking for a low resistance. If you find one that goes to infinite or extremely high. There is a problem, most likely a break, in the wire.
To use the voltage portion of the meter, switch to the first setting.
When measuring voltage, simply ground the black lead and place the red lead on the portion of the circuit where you expect there to be power.
So to check a switch, measure the input to ensure that voltage is reaching the switch. Then place the red lead on the output. With the switch off there should be no voltage (Or infinite resistance if measuring ohms). Now turn the switch on. Voltage should flow through and give you a 12v reading across it. Once you have ensured that the switch functions properly,and is receiving power. Move to the object which receives power from the switch. Place the red lead at the input. You should see 12v flowing into the object, coming from the switch. If you don't have power (or infinite resistance in the wire) there is probably a break in the wire. If you don't have power, but DO have continuity, there may be a short present.
I don't have enough knowledge of the wiring in the bike to tell you where to check, but hopefully that helps you understand what's going on.