Here's what I had to do...
What's up Austin... First question: Do you have the NEW BODY style Explorer or the older style? If it's newer, follow below.
I have a '96 Eddie Baeur w/ Premium Sound and if it's anything like mine, you'll have a fun time figuring it all out in your head how it works, but here's how mine is put together:
Headunit:
Square Black Plug with 8-Wires being used with 16-Hole Locations in it + a Long Grey Rectangular Plug with 7-Wires being used with 8-Hole Locations in it.
Here's the fun part, I DO NOT RECOMMEND CUTTING WIRES where the stock radio harness was at, because sometime down the road you might want to hook things back up the way they were (I know I do someday). However, on the above 2-Plugs I was talking about (Square Black and Rectangular Grey), you'll only actually need to run a Harness from this Grey connector to some wires of your aftermarket radio.
Speakers:
You mentioned you have the PREMIUM SOUND SYSTEM in your Expl. If this is so, like it is on mine, you have a Sub in the rear-right panel with 2-amps as well (one for sub + one for speakers). The amp on the LEFT side of that panel is the one for the speakers (all 4 of them). On the left side of that amp, there should be 3-plugs: 2 that are right next to each other and one that has about 13-holes in it with 8-wires across the bottom of the plug. Those 8-wires are your SPEAKERS! (it took me the damn longest time to figure that out through research with Ford). You'll need another Harness to PLUG into that BLACK 13-Pin Plug and run it up to the aftermarket Radio. Now, on the harness that was supplied with your aftermarket radio, you'll need to make the necessary connections (I used butt-connectors) to hook everything up (from the Rectangular Grey Connector which supplies 12V Switched Power, 12V Constant (Memory) Power, Illumination/Dimmer, etc. (I have all the paper-work on my stereo as in which wires go to what function, as long as you have the same system I have).
In-Dash Harness:
Yes, you will need an in dash harness for your Single-DIN sized aftermarket Radio (probably the one with a pocket).
I hope this helps you out... and if u need more detailed instructions I can provide them since I did EVERY last detail myself on my Expl.
Talk with u later...
-Mike