Ok, once you've got your harness layed out in front of you, preheat your soldering station to about 550-650 depending on what tip you're using.
You're going to need to tin Each individual wire, and then solder them together neatly. Make sure you use shrink tubing! Do not use electrical tape, it will slowly start peeling off and then you'll end up shorting you expensive sound system!
Once you're done with that, open up your hood and unplug the black wire to prevent and damage. Undo the two screws under the cup-holder, and gentle pull it out. Then the trim going around the stock system and AC vents needs to be lightly pulled off so you can access the 6 screws holding the stock stereo in. Once you undo the screws, pull the unit out and unplug the antenna, powersupply, and whatever else is plugged in. Take off the mounting brackets on the side, set them aside. Then take of the mounting bracket from the unit you bought, and put the bracket from the stock unit on the new one. You may only be able to get three screws on each side, and that will be enough to hold it in.