I am going to install 6 Day-Brite Lighting HID lamps CAT. NO. EHL 400M5T-LR20-LP-UP in my garage that is 40X60. There are 6 wires coming from the transformer and one ground attached to the case. The following is written on the wires:
COM
120 V
208 V
240 V
277 V
480 V

How do I wire these lights beginning at the breaker box? I would like to use these as efficiently as possible. Thanks for the help.

You most likely have 240 volts in your garage. If so, then connect one supply lead to the common, and the other to the 240 volt tap. Be sure to securely cap all the remaining taps on the ballast.

Using different voltages does not make a light operate more efficient, other than using a higher voltage allows less copper and more lights to be connected to one circuit.

Ok, So I have decided to run the 240 volts. I have wired other 240 appliances and such and there are 2 poles on the breaker. In order to receive 240 there must be two hots. Do I hook both hots together to get the 240 to the one tap?

No, you hook one to the 240 tap and the other to COM (common).

If you connected both hot supply leads to one input wire the circuit would be shorted. I get the word "common" is confusing you, the wire is called common, as it is common to the five tap input leads.

Imagine the common is one entrance ramp to a highway, and the five taps are five separate exit ramps.