First, take a look at the pinout for the DC barrel jack that's in your kit:
The GND and V+ pins are pretty straight-forward; when connected to our 9V DC power supplies they will be 0V and 9V respectively. That crazy pin in the center is a bit more complicated, but it can be very useful at times; we'll come back to it...
First, that third pin can make it a bit confusing to connect the jack to a breadboard, so here's how to hook it up:
Notice the two wires at the bottom. These connect the two red power rails together, and the two blue ground rails together. Unless using multiple supplies (for example you could have 5V on one side and 3.3V on the other), you'll almost always want to do this so that components on either side can be easily connected to the power supply. (Note that if you are using different supplies on either rail, you'll almost always need to connect the ground rails together!)
Now about that third pin on the barrel jack...
Imagine you had a circuit that you sometimes wanted to power with a battery, and sometimes with a wall adapter. You couldn't have both connected at the same time, so you'd have to disconnect the battery every time you plugged it into the wall. This could be done with a switch, which when switched one way would connect the battery to your circuit, and the other way would connect the barrel jack to your circuit. The problem with this method is that you would have to remember to flip that switch every time you changed power sources. The purpose of the third pin on the barrel jack is to switch sources for you. If a battery is hooked up with its positive lead connected to the barrel jack's positive pin, and its negative lead to the barrel jack's 'switch' pin, then when the power adapter is not plugged in, the battery will be powering your circuit, and when the power adapter is plugged in the battery's negative lead will be disconnected from your circuit, and the power adapter will be powering it.
A regulated 5V supply
The above circuit certainly gets power to the breadboard, but nine volts is a bit high when it comes to a lot of the stuff we'll be doing in this class, especially once we start playing with the Arduinos, which expect 5V and can easily be fried by 9V. Luckily there is a wonderful device called the voltage regulator which, believe it or not, regulates voltages. In your kit there are a couple LM7805 5V fixed voltage regulators. What this device does is it takes in any voltage that is in the range of 6.5V-25V, and outputs a steady 5V. (Note that it does this by turning the extra energy into heat, so as the input voltage gets higher it will get hotter, and will need a heat sink for higher voltages.)
The voltage source V1 will be our 9V power supplies, connected through the barrel jack. Note the 0.1uF bypass capacitor (C1). This circuit looks something like this on the breadboard:
