I have an '87 CRX that would not pass california smog (failed 15 times and barely passed on 16th). The problem was Honda tried to regulate how much air went into the carb vs regulate the amount of fuel. I will spare you the reasoning to never try and rebuild the original motor. Just know, it is not recommended. If you do attemp this project I highly recommmend three items; an '86-'89 CRX, an '88-'89 integra (junk yards and craigslist are full of non running ones), and manuels for both. This is not just an engine swap, we are going fuel injection and making what i call my T-Rex (mix of the names Teg and CRX. In the end, I get 35 mpg average if I keep my foot out of the gas petal and have seen 41mpg.
Step 1: Completely Dissasemble Donor Car
Start with taking pictures of everything. Where parts are located and how they connect (makes it easy later if you get stuck). Drain all fluids (if it has A.C. have the coolant removed professionally.) Now start disconnecting the electrical. Very important that you mark both sides of each connection. I used painters tape and a sharpie. Inspect every part for wear and reusability. After everything is disconnected and marked, start removing everything around the motor. Keep the mounting hardware with each part. Clean each as you go and replace broken parts. Now pull the motor and tranny. Completely dissasemble and clean everything. The manuel is a great asset to individual part dismemberment. Now remove the shift linkage, brakes front and rear (include the distribution valve and master cylinder, and e-brake cables), and the front/rear suspension. Remove all electrical. Don't forget the fuel pump and fuel lines.
Step 2: Rebuilding Your Donor Parts
Now it is time to rebuild the parts going into the CRX. This engine was in very sad shape. I lapped in the valves by hand. Simple procedure. Autozone sells a cheap kit to complete. (newer motors are not so easy and should be done by a shop). Replace all bearings, seals, and bushings. (quality parts are worth every penny... I learned the hard way). Everything should be like new when putting it back into the CRX. Items like shocks and water pump should just be replaced.
Step 3: Parts Ready? Swap Time
The CRX was off the road for two weeks. I recommend backing into the garage for ease of access to the front. Put the entire car in the air on four jack stands. Anything that you removed from the Integra remove from the CRX but don't throw it away just yet. (I needed some of the hoses and mounts that were in too bad of shape on the teg) Once everything is removed completely clean the entire car.
Step 4: New Parts Time
Start in the back and work your way forward. I recommend getting a fuel take from a CRX Si (it was a larger tank and had baffles for the pressurized system). Run the fuel lines and brake lines. Install the rear brakes and suspension ( now I have disc rear brakes). Installed fuel pump inside the cabin just behind the driver seat. Install all electrical wire harnesses. Install front suspension and brakes. Now it is time to install the motor / transmission. The cars are very similar and this is a bolt in procedure.
Step 5: Gauges.
There are several possibilities for what gauges you use. I recommend reading all of the articles posted on redpepperracing.com to choose what will work for you. I chose to custom build my entire cluster (speedo from 91 civic, tach from 88 teg, fuel and water from 87 crx.) custom built trip meter and circuit board.
Step 6: Testing and Trip to Bureau of Auto Repair for Certification
Two weeks after pulling into the garage (still worked normal 40hr weeks) she's back on the road and scheduled to see the referee. Great part is she passed on the first time and was so clean on the smog. One less junker on the road and the total cost was less than $3k. I recycled the integra and remaining parts. I am now the proud owner of a fuel injected '88 integra that looks like a CRX. Stiff suspension and all wheel disc breaks. I get 35mpg, reliable, and it is very quick.