Note: I'm using my '92 as the example for this, but the big thing is to use a dash that matches the year of your car.
Step one is to get the wiring diagrams. The one for my car is here: http://oskin.ru/pub/chrysler-dodge/manuals/Service Manuals/1992_AX_Acclaim_Dynasty_LeBaron_Shadow_FifthAvenue/92FWD_8W.PDF
Yours may be different.
Step two: Get wire. Lots of wire. (Not really lots, but it will make life easier when extending wires from the right to left side of the cluster.)
Step three: Get the digital cluster AND BCM from your donor car. The mileage will be incorrect, but if you don't grab the BCM, you'll find that your water temp, oil pressure and possibly fuel level will all be incorrect. Not only this, but on a Dynasty with the single-connection BCM, you will have the most godawful, irritating constant tone from key-on until you pull the battery. Get the donor BCM. I learned this the hard way. Also, don't forget the little lightbulb on the pigtail to light up the PRNDL indicator. It's a good idea to go ahead and change all the bulbs while you're at it. I used green dimmable 194 LEDs from a local supplier, here in Missouri. You can test by connecting pin #7 to ground, and pins 2 and 11 to 12V. Remove the brake warning bulb, because it'll be constantly on, with a non-ABS car and an ABS cluster.
Step 4: It's a good idea to disconnect the battery, here. I recommend doing this in a well-lit garage, and have a lamp with a flexible head to point at your cluster area.
Step 5: Yank the cluster out of your car. I'm not going into this process in-depth, because it's pretty self-evident. Just pull the five screws along the top, pull the trim piece off and then the four screws to hold the cluster in. Should go just like your junkyard pulling did, but with slightly more care.
Step 6: Once you're clear, you should have two plugs there. Go ahead and cut these off.
Step 7: Let's get the hard part out of the way, now. Namely, the adding wires where they didn't properly exist, before. From the "L" shaped plug, you want to run the grey-yellow across the car to pin #11 on the red plug of your donor BCM, and the violet-yellow wire from the round plug, to pin #24. This will get you your oil pressure and your temperature sender feed. Then, go ahead and plug the BCM in.
Step 8: If you haven't done so already, go ahead and pull the panel covering the radio bolts, and unbolt the radio, sliding it forward until you can see the connectors. Tap into the pink/light blue wire, and extend it into the instrument panel cavity. This will get you the "courtesy light" feed that you need. Another lesson I learned the hard way.
Step 9: Play contortionist for a few minutes, get upside down under the dash and tap into the violet/brown and the white/black wires on the diagnostic connector. Make sure to run them, in twisted pair, up through the dash and have them pop out inside the cavity.
Step 10: At this point, you can simply match the colors. You DID make sure and get plenty of pigtail, right? For the wires you extended, make sure you marked them with the original colors, if you didn't use the same color wire as the original. You can also add in the little 194 on a lead now, again matching colors. Heat shrink over all soldered connections.
Step 11: Reconnect the battery and turn the key on. With luck, it should all light up. Make sure all your readings are decent, then start the car. Test the functions, and if it all works, just button it back together and take it for a test drive.
Here's mine, after I put in the cluster. (Note: Mine is currently using the original Dynasty BCM, because I don't have a digital cluster Fifth Avenue/Imperial one. Because of this, I had to pull the BCM apart and cut the wires to the piezoelectric chime to get any sanity while driving. Don't do what I did, get the donor car's BCM.)