Rewiring power and ground to head unit

Before I move forward with purchasing a new head unit (thanks for all the tips), I figure I'll give mine one more shot to perform worth a crap.

I did some searching on here and saw that some people have had the same issues I've had with the stereo clipping out and then coming back on a second later, and most of the issues seem to be related to a bad power and/or ground to/from the head unit.

So the question is, how do you re-run the power and ground wires from the head unit directly to the battery?

I know there is a wire harness in the back of the head unit, but how do you pick out the right ones? And do you just splice into them and run a dedicated line directly to the battery terminals or what?

thanks once again.