Most modern frames have a socket welded to their seat tube that the front derailleur is bolted onto. Most front derailleurs also come in a version that can be strapped to the seat tube if the socket is missing. The derailleur should be adjusted such that the cage is parallel to the chainwheels, and just barely clears the tips of the teeth of the chainwheels as it is shifted back and forth. There are two screws in the body of the derailleur that limit the movement of the derailleur. This prevents overshifting, which would throw the chain off the chainwheels.
Rear derailleurs are available with three different cage lengths (i.e. the distance between the pulleys). The length is called the capacity, and is measured in teeth difference: add the numbers of teeth of the largest chainring and the largest cog and subtract the numbers of teeth of the smallest chainring and the smallest cog. You can exceed the specified capacity of a rear derailleur by a couple of teeth but not more, or the chain will become stuck in unpleasant ways. For standard road bikes, my feeling is that you should stick with the shortest (racing) cage and adjust your chainrings and cogs because longer cages reduce shifting accuracy and make the chain bounce more easily on rough road surfaces. Many high-end rear derailleurs are available only with short cages.
It is absolutely critical to adjust the limit screws of rear derailleurs precisely. If the chain overshifts and falls off the smallest cog, it may block the wheel. If it overshifts at the other end, the derailleur might get caught in the spokes, which will probably crush or snap the derailleur in half and bend the dropout of the frame. A good mechanic may be able to bend the dropout back into shape (this requires special and very expensive frame alignment tools) but this is an excellent way of destroying frames.
Rear derailleurs must match the shift levers, or the gear spacing clicks built into the shift lever won't be translated to the correct cog distances by the derailleur. The result is a rattling noise in some, perhaps most, gears. There is an adjustment screw where the shifter cable enters the derailleur body. Adjust it so you can smoothly shift between the middle two cogs, then test with the whole range. After each adjustment of the screw, shift at least once. I have found it to be impossible to adjust until the chainline looks (and sounds) right and then do the next gear. Always keep shifting during adjustment. This is actually a simple procedure.
Don't bother with special sealed-bearing pulleys. Pulley friction is not a problem, and if the width of the new pulleys doesn't match the width of the original pulleys, the ends of the screws that hold the cage together might either hold the cage together poorly, or worse, stick out and catch the spokes with the usual catastrophic effects. Instead, clean the pulleys regularly, the accumulated gunk makes a much bigger difference. By the way, the back plate of the cage must be installed with the bigger end pointing down, or the chain will keep falling off the lower pulley.
See also an article on "Saddle"
