Welcome to the site.
It sounds like whoever installed the stereo decided to do a hack job and not use a wiring harness.
If there's no grey or black plastic square things that a few wires go to, then you'll have to either just hard wire the new stereo to the old wires (which I assume is what you want to do), or wire up a new factory harness.
To know what's up with the stereo though, first you need to find out which stereo system you have in the vehicle. Some 91-94 Explorers have a stereo system with an amplifier behind the rear passenger side interior panel. You can look through the hole in the panel the seatbelt goes through with a flashlight, and see if you discover a big silver or black box.
If there's no amp back there, you can just wire up the stereo as just about any other, with the standard wire colors and connections:
Yellow Wire - battery (constant power wire)
Red Wire - ignition (no power with key off, power when key turned to ACC or ON)
Orange Wire - Illumination (power when lights turned on)
Black Wire - Ground
The other wires, either green, purple, white, gray, etc are the speaker wires. The wires with a black stripe are the negative wires.
If you have an amp back there, the only big difference is that you'll need to connect the blue wire (either solid blue or blue with a white stripe) to the amp turn-on wire on the stereo (usually also blue). However, this means that the factory amp is now powering the speakers, and doing it with a signal it gets from the aftermarket stereo amp. Basically, you're sending an already amplified signal to the amplifier. Not good.
What you'd probably want to do if you have an amp is get an adapter to either bypass the factory amp (autozone sells these for $20 or you can get them online for less), or get an adapter to use the aftermarket stereos pre-amp outputs to send a signal to the amp, instead of using the speakers.
Post back here once you've figured out which system your vehicle has and you can get more specific details on your options.