Get a tester.
Find the wire that has power all the time (with the key off) and hook that up to your constant 12v for your radio.
Find the wire that has power with ignition (with the key on) and hook that up to ignition.
Get the black wire from your radio and hook it up to the ground from ur car. If you can't find that, turn ur ignition on and touch the black wire on metal surfaces behind the radio until it comes on, you've now found a ground. Attach it somehow and you're set on the power.
Now that your radio has working power. Go into ur radio settings, fade the radio to the front and then balace it all the way to the left. Now get your front left speaker wires from the new radio, test the speaker wires on your car until the front left comes on. When it does, attach them. Do the same for the remaining speakers.
**Note** Let's just say that your car's speaker wires for the front left are Grn/Blu , and then Grn/Blck ... And let's say u use grn/blck for negative from your new radio and grn/blu for positive.... Use ur common sense on the other speakers.... if the next set is Gray/blck , and gray/blu you're gona wana use the same pattern, use black for negative so all your speakers play in phase.
This is how i did it back in the day b4 i knew about the wonders of wiring harnesses =) When I was a broke 16 year old.