How do I install a new stereo in my 94 Toyota Tercell?

I bought a new Stereo deck for my 94 Toyota Tercell and I cant seem to get power to it. The color of the wires are different and also have extra mystery wires left over. I have looked up diagrams but none seem to help get power to the deck. I am not using an amp because the speakers are low volt. Any suggestions?
 
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