brake bleeding
I also have a gen 2 Integra, no ABS, which I prefer. You are correct in starting with the brake furthest from the master cylinder, the right rear. Then move to the left rear, right front, left front. Most people (including me at one time) neglect their brakes and don't bleed the brakes until their is a problem and they are fixing other things. Brake fluid absorbs moisture, and really should be bled every couple of years, at least. This will prolong the life of the master cylinder, wheel cylinders and calipers. Also, I always take some paper towels and soak up all of the old fluid out of the resevoir and refill with clean fluid. Bleeding is quicker this way, as you are only purging the fluid in the lines, not a whole master cylinder full of dirty fluid. Be sure to have a trash can or something under the hood to catch the towels and dripping fluid, to keep from ruining your paint. If all you are doing is bleeding the brakes, it is not necessary to remove the wheels. If replacing pads, shoes or other repairs requiring the wheels to be removed:
***BE SURE WHEN WORKING UNDER A CAR WITH THE WHEEL OR WHEELS REMOVED THAT IT IS SAFELY SUPPORTED WITH JACK STANDS, NOT CINDER BLOCKS OR SOME OTHER RIGGING. GOOD JACKS ARE WORTH THEIR WEIGHT IN GOLD, UNTIL THE DAY YOU CAN AFFORD A LIFT***
You can even bleed the brakes by yourself, in case you pissed your girl off one time too many (like me) and can't get the neighbor kid to calm down long enough to pump the pedal for you. First, figure out what size rubber hose will fit over the bleeder screw. I have used clear hose from Wal Mart, aquarium tubing, I think. You'll need about three or four feet of it. I take an old plastic soda bottle, drill a hole in the cap just big enough for the hose to fit in. I also take a 18"-24" long peice of small guage solid wire, #18-#22 or so, since it is easy to wrap. (I have a lot of fixture wire out of flourescent light fixtures laying around, since I am an electrician), tie wire or such works good as well, to hang the bottle and keep from knocking it over and making a mess. I promise you will knock it over at least once if you don't do this. I did. Tie one end around the neck of the bottle. I like to take a box end wrench six point socket or line wrench and be sure I can break all of the screws loose before I start (10mm on every Honda/ acura I have worked on). Next, put about 1" of fresh brake fluid in the bottle so that the brakes won't draw air while you are bleeding them. Insert one end of the hose into the bottle with the end about 1/2" from the bottom. Find a good bracket or such to hang the bottle on. Make a loop in the other end of the wire you tied on the bottle and hang the bottle on the bracket,etc. Loosen the bleeder screw about one turn. Insert the other end of the hose over the bleeder screw. Be sure the resevoir is full, and to keep the resevoir full of fluid, and put the cap back on it everytime before bleeding.(It is easy to forget if you get in a hurry) Brake fluid could gush out and RUIN your paint. Get inside and pump the brakes SLOWLY and steadily. After about four-six pumps, check the hose to see if the fluid is clean and has no air bubbles. The fluid placed in the bottle when you started keeps air out of the system. This is also why you don't want to put the hose touching the bottom of the bottle, as it will suck up the old dirty fluid you just bled out. Also, bleed the brakes until the nasty fluid is out, not just the air bubbles. If the fluid looks clean and has no bubbles, you can take the hose off, tighten the screw and move on to the next wheel . Be sure to check the fluid level again, or you are wasting your time. If you have trouble with air leaking past the bleeder, you can take the bleeder screw out an smear a little grease on the threads and screw it back in. This will help it seal when bleeding, and keeps it from getting stuck the next time you need to bleed the brakes.
As for doing anything different on ABS vehicles, on my 97 chevy truck, I had to use a Mity Vac to bleed the brakes to get a good solid pedal feel. I bled the brakes the old fashioned way about 4 times, seemed to get the air out, but still had a soft pedal. After the Mity Vac, I had my good pedal feel back. Good luck!