I'm trying to put a radio in my 83, the previous owner took out the radio he had in it and left us a mess,we went to best buy and bought an alpine head unit and a wiring harness. Question is where does the wiring harness go.

 

Your wiring harness should match up to the "mess" you see.

There should be 12 or so wires. (and should be labeled on your harness)

Red and black = power and ground.
Blue (watch out, there are diff shades) = remote.
Yellow/orange = light dim

The rest are going to be front left/front right, rear left/rear right speakers.

There's most likely a diagram in the head units instruction manual explaining the different wires.

 

Hopefully by "mess" you dont mean that he cut off the existing harness. If thats not the case, its pretty simple:

For the harness you bought, you wire it up to the head unit you bought, most of the time you just match the colors, but sometimes they can be different, so make sure each wire goes to the right place by looking up a wire colors for your car and matching them to whats printed on each wire of the new harness...heres the list:
http://www.the12volt.com/installbay/...etail/482.html

Once youve wired your new harness to your aftermarket radio, it should just plug in to the existing stereo harness where the old radio was, and everything should work.