What is the easiest and most efficient way to cut a 45 degree angle into a piece of wood?

Are you trying to figure out how to get the 45 degree angle,or how to cut the 45 degree dado?

For figuring the angle, measure along the piece a certain distance, then measure that same distance at 90 degrees from the first measurement, draw square lines from these two points. You have made a square, now draw a diagonal of this square and that is your 45 degree measurement.

For the actual cutting, from what you describe, you want what is called a "dado". You can cut this with any of the following - a radial saw, a circular saw, or a router, all set to the desired depth of cut.

Try clamping the board down to the table of the chop saw to keep the wood from moving either left or right while cutting. I have seen the material being cut try to migrate while the saw is cutting before. Make sure to put something between the clamp and the wood so you don't dent it. If that isn't it then check the saw and see if the blade is 90 degrees with respect to the table. Check to see if the blade has any play in it by grabbing the blade (saw unplugged) and wiggle it left and right. There should be almost no play. If anyone (like the crew) dropped the saw or knocked it over once, then you should also check that the blade is at 90 rwt the table while down.

Go to the hardware store and buy a mitre box ( 6-10 dollars) You can control the depth of the cut by eye. This is the cheapest and most accurate way other than buying a professional mitre saw

If you don't know how to do it, chances are, you don't have the equipment to do it either.

Your best bet is to take the piece of wood to a cabinet shop, and explain what you want. They would do it cleaner, faster, and safer than you could.