Originally Posted by
Phil_gretz
^^agree. Remove rear wheel. Break chain. Unbolt derailleur cable anchor. Remove rear derailleur. Disassemble pulley cage assembly. Clean entire derailleur. Grease pulley sleeves. Reassemble derailleur. Lube all pivot points on derailleur, all threaded parts. Exercise. Wipe off excess.
No need to break the chain; it's free as soon as you remove a pulley and loosen the bolt on the other one.
No need pull the wheel and RD off either, unless you get into a cleaning frenzy. The chain only cares about the rings, cogs, pulleys and inside of FD and RD cage plates.
You might prefer to remove the wheel rather than derail the chain off the ring to give some chain slack though, or you could just master the technique of replacing the pulleys with the chain in place; not real tricky.
Screw the upper pulley on, leaving the bolt loose enough for the inner cage plate to swing. Rotate it so the tab allows the chain through, then place the lower pulley against the chain and push it into position, while sandwiching it between the cage plates and holding the outer plate forwards with your other hand. It should be pretty easy to line up the holes so the bolt can go in; you can let go when you get it started in the thread.
All this in small/small, of course.