This is far from being 100% accurate. This is simply a quick guide to prepare you for what you're about to get into. Follow the owner's manual for a clean install.
What you'll need:
Stereo Removal brackets (~$3)
Wire harness for an aftermarket radio (~$9)
electrical tape (~$1)
aftermarket radio dash kit (~$20)
Your wording was a little hard to understand, but i'll assume that you have an Explorer with the stock 1.5 DIN radio (the big stereo...like 6" tall).
1) This part is a little fuzzy b/c it's been so long since i've had the factory HU, but i think you'll need to use the stereo removal brackets and slide them into the side of the stock stereo. Do what is necessary to remove the radio (remove screws if need be)
2) disconnect the wire harnesses that plug into your stock radio.
3) connect the new harnesses to the existing wiring harness that used to go into your stock radio. You will have bare wire ends on the new harnesses (or they'll be covered up with pre-cut ends).
4) Twist/crimp the appropriate wires from your *NEW* Sony radio harness into your now-extended stock harness. Make sure the connections are solid and that you wrap them tightly with electrical tape.
5) There is probably a second harness for your speakers...there shouldn't be any crimping/twisting of any wires. It should all be plug-and-play.
6) Plug the harness into the head unit to verify that everything is in working condition before you proceed.
7) Unplug the head unit (HU).
8) install the plastic dash kit. You may have to connect some of the plastic together (like the lower pocket to the frame of the kit).
9) Reconnect your harness to the radio. Slide the radio into the dash kit.
10) install any trim for the radio
11) you should be done....good luck
-=bmacd=-