How do hook this reed sensor to Arduino?

Do I need to input a power supply to this? brown terminal is positive? blue is negative ?
Those take up the two wires, how would I plug this into an Arduino? Using a breadboard? How would I do so?

I tried just hooking one end to an Digital Pin and another to the 5V but the light doesn't even turn on when I put a magnet near it.

Do NOT connect a power supply across the brown and blue wires.
You need to get a meter and put on ohms or continuity scale across the brown and blue wires. And see if it shows 0 ohms or continuity with the magnet next to it. Once we verifiy that we can proceed

It's just a switch.... doesn't need power: it's either open or closed. As raschammel says, test it with a meter first.

It's usually easiest to configure a switch to a digital pin on one side, and to ground on the other. Then code the sketch to use the internal pullup resistor. The, when the reed switch is open the pin will read high; when closed it will be low.

Have a look at this example.

As far as this goes:

I tried just hooking one end to an Digital Pin and another to the 5V but the light doesn't even turn on when I put a magnet near it.

.... we would need to see what sketch you have running.