Swapping the bumper itself is fairly straight forward. You need the bumper supports (#24), the bumper cover and it's metal backing(#2-29), the bumper to bumper supports mounting screws (#78 ), and the bumper support to car mounting screws (#73-74). While your jacking this off some poor unsuspecting car you will also want to grab the turn signals, running lights, and fog lights (along with their plugs). Make sure to cut as much of the harness as you can get so when you are wiring them into your system you won't have to lengthen the wiring.
This sounds kinda complicated but it's not at all, just remember to collect all the screws you take off the car in a plastic bag.
Now for the fun part, wiring. All though not very difficult either, it is slightly confusing as the 88-89 bumpers have two sets of turn signals and the 90-91 bumpers have one set. Make sure you have a tester light, they're cheap (around 5 bucks at autozone) and make your life easier.
A word of warning, when you cut the plugs off of your car and expose the wire be careful not to let the bare wires touch each other, you run the risk of blowing a fuse and confusing the crap out of yourself when none of your lights come on. (not that it happened to me ....)
First find out what's what on your wiring harness, if you didn't take mental notes when you took off your 90-91 bumper here's a refresher.
Now we need to identify the lights, I thought this would be the easy part but quickly confused myself when I realized that I never really looked at what lights light up when on an 88-89 ... So once again I've got you the hook up.
Well once you've got that all sorted out, hack the plugs off your 90-91 harness (remember, no touchy touchy) and grab up your plugs for your 88-89 lights. I ran into one stumble that didn't seem to effect anything, but confused the crap out of me. The running light on the passenger side of your old 90-91 lights had two ground wires (the black ones) running to it. I tested with my handy dandy tester light and one seemed to do nothing and one acted with the running light, so I just capped the one that did nothing. You can do the same or do some research and find out it's purpose, but mine works fine right now so I'm leaving it be.
Alright now you need to wire everything together. Check out the diagram and then have at. Since two of the center lights are turn signals it is prudent to lengthen the wires running from the turn signal/running light combo so that you have enough room to stuff everything back in the way it's supposed to go. If your wires happen to be different colors than mine it's easy enough to adapt, since we IDed the different lights just look at the colors running to them and change accordingly. Remember, black always goes to black.
Here's my completed bumper swap.
Good luck and if you have any questions or I did something stupid that might result in an exploded car just let me know.