Lets start with tools. What kind of tools do you have? If you're going to get into mobile audio then there are a few tools you're absolutely going to need.
Sta-Kon crimpers for insulated and non-insulated connectors
A good pair of wire strippers, not some Wal-Mart garbage
A pair of needle-nose pliers, you can go cheap on these
An all-in-one (or 10-in-1) screwdriver with philips, flat and star drives
As for material, you'll need some
Butt splice connectors (red and blue)
Female spade terminals (red and blue)
Electrical tape (3M Super 33+ is the best)
6" tie wraps ("zip-ties")
The first thing i'd do is butt-splice the wires coming off those rear deck speakers back together with the ones hanging there. Get a 9-volt battery and go up to the front and find the + and - colors that go to each speaker and 1 speaker at a time touch the + and - of the battery to the + and - wires for the speaker. Listen for a thump or a pop sound as you touch the wires to the battery terminals. If you hear noise coming from the speaker then its good and you can move onto checking the next one.
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