Derailleur Adjustment

Chain
Rear Derailleur
Front Derailleur
Gripshift (for road)
Problems
The "RBR Way"

Chain

Technically the first thing to do, before adjusting the derailleur, is to correctly install a chain, including sizing it properly. A primer for properly adjusting chain length can be found here.

Rear Derailleur

Recognize the important elements of the derailleur: the high & low adjustment screws, which only keep the derailleur from running the chain too far toward the spokes (low gear adjustment screw, or into the gap between the highest gear and the frame (high gear adjustment screw); the barrel adjuster, which slightly tightens or loosens the cable, allowing you to micro-adjust the derailleur; and the derailleur cable, which you will rarely have to fuss with after its initial mounting.Unscrew both the high & low adjustment screws on the derailleur body, not so much that they fall out of the derailleur, but enough so that they won't impede the derailleur's travel, and then screw in the high gear screw so that the derailleur pulleys are lined up just a little to the outside of the small cog.Put the chain onto the small chainring.Turn the shifter so that the chain is on the smallest (most outside) cog.With the barrel adjuster screwed in as far as it can go (hand tight), the cable should be as tight as possible while allowing the derailleur to rest unsprung. The best way to achieve this is to pull the cable relatively tight without putting pressure on the derailleur, and tighten the cable down.Shift the derailleur to the next cog. Three times out of four it'll go in easily, but if it complains a little, unscrew the barrel adjuster a little, and it'll slip right in.Go through the gears, make sure all is smooth, do a little micro adjusting on the barrel adjuster as needed.Screw down the low gear adjustment screw with the chain on the largest cog. Give yourself a tiny bit of extra room on this adjustment, if you turn this screw down to the correct amount on the workstand, that might be a quarter turn too far when the bike is on eh road. You'll find this out right when you need this gear the most, which is on a steep hill twenty miles from home, (which is coincidentally where your phillips head screw driver is).

Front Derailleur

Mount the derailleur so that the cage is as close to the big ring as possible, and is parallel to the frame (the cage should be straight front to back, not angled in or out).Same as above on the high and low adjustment screws.This can be a pain in the ass, because there is no barrel adjuster on the derailleur, so you have to get the cable tension exactly correct. However, you may have a barrel adjuster elsewhere on the bike, like on the downtube. This is the case if you have either Gripshift, STI, the Syntace shifting system, or other. If you do have such a barrel adjuster, make sure it is screwed down all the way, hand tight.This time you'll start with the chain on the largest (most inside) cog.Pull the cable until it is tight, with the inside of the derailleur cage about an eighth of an inch from the chain.Tighten the cable down, and screw in the adjustment screws so that the chain, doesn't derail on the outside or inside.You should have only a small amount of clearance between the chain and the inside of the derailleur cage when the chain is on the small cog. You should also have enough clearance on the outside so that the cage doesn't hit, or even come perilously close, to the crank arm as it comes swinging by. If either of these is the case, or if you have a problem derailling, your derailleur may be mounted incorrectly on the braze-on.

Gripshift: the following is a reprint of a post the editor put up on rec.sport.triathlon

Front Gripshift actuators have 4 positions. The two inside positions are trim (micro adjustments) while the chain is on the small chainring. The two outside positions are for trim on the large chainring. The "click" from the second to the third position changes the chain from one chainring to the other.Often what happens with Gripshifts is that they are adjusted so that they are one click off, that only three positions are available instead of four. For example, the cable tension, and high/low adjustment screws on the front derailleur, are set so that the inside trim adjustment is actually the "click" that derails the chain up to the large chainring. You might think this would give you two further outboard clicks while on the big chainring, but in reality that wouldn't happen, as the high gear adjustment screw would be turned down so that only one click is available (if it were not turned down, limiting the amount of outside travel on the front derailleur, the derailleur cage would hit the driveside crankarm.This must sound terribly confusing. The net result of the above is only one Gripshift position while the chain is on the small ring, and two when it is on the large. This will inevitably cause the chain to rub on the inside of the front derailleur cage while the chain is on the most inside cog(s).The same problem can happen in the other direction as well, with no ability to trim the derailleur while on the large chainring.The way to avoid this is to unscrew both high and low adjustment screws all the way, and make sure all 4 front derailleur positions are available. If they aren't, the cable is either too tight or too loose (it's pretty easy to tell which is the case). When all 4 positions are working, adjust high and low screws appropriately. Even on a "short" chainstay bike, so long as the chainstay length is at least 38cm, c:c, you should not have a problem.If you still do have a problem, either you have a bad chainline on your bike, meaning your BB axle is probably too long or short for the crank you are using, or you had a 7 speed bike that you turned into an 8 speed, something like that; or you have a Gripshift actuator with the cams cut wrong, which does happen; or else there is some other problem which I can't diagnose without having the bike in front of me.

Problems

The rear derailleur shifts well over half the cogs, but is "out of alignment" on the other half: you may have: (a) an 8 speed shifter on a nine speed cogset, or the reverse, or a seven on an eight speed, or such mis-matched combination.; (b) you have an Ultegra shifter on a Dura Ace derailleur, or the reverse (Ultegra, 105, RX100, derailleurs and shifters should all be interchangeable, but none of these interchange with Dura Ace, except the new 9-speed stuff, in which Dura Ace and Ultegra are compatible with each other).The rear derailleur will either shift up smoothly, or down smoothly, but not both: you've either, (a) got a lot of oiling and cleaning to do; (b) got a cable to replace, or, (c) got an old derailleur that has a worn out spring, and needs replacing.The dang Gripshift doesn't shift well: you've either, (a) not followed the directions above, or, (b) got a Gripshift in which the cam wasn't cut correctly.

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SIS Adjustment Procedure From: Bob Fishell, reprinted here from the rec.bicycles.tech FAQ

Shimano's instructions for adjusting SIS drivetrains varies from series to series. The following method, however, works for each of mine (600EX, 105, and Deore'). [Ed note: Works on Exage road and mtb also.]Your chain and cogs must be in good shape, and the cable must be free of kinks, slips, and binds. The outer cable should have a liner. clean and lubricate all points where the cable contacts anything.SIS adjustment:Shift the chain onto the largest chainwheel and the smallest cog, e.g., 52 and 13.WITHOUT TURNING THE CRANKS, move the shift lever back until it clicks, and LET GO. This is the trick to adjusting SIS.Turn the crank. If the chain does not move crisply onto the next inside cog, shift it back where you started, turn the SIS barrel adjuster (on the back of the rear derailleur) one-half turn CCW, and go back to step 2. Repeat for each pair of cogs in turn until you can downshift through the entire range of the large chainwheel gears without the chain hesitating. If you have just installed or reinstalled a shift cable, you may need to do this several times.Move the chain to the small chainring (middle on a triple) and the largest cog.Turn the cranks and upshift. If the chain does not move crisply from the first to the second cog, turn the SIS barrel adjuster one-quarter turn CW.If the drivetrain cannot be tuned to noiseless and trouble-free SIS operation by this method, you may have worn cogs, worn chain, or a worn, damaged, or obstructed shift cable. Replace as needed and repeat the adjustment.