Well, the gist of the clones and stormtroopers is this:
The original clone troopers during the Clone Wars were all cloned from genetic material of Jango Fett by the Kaminoans and trained by a hundred hand-picked (by Jango Fett) mercinaries, 75 of which were Mandalorians; this combination of good breeding and training over a ten-year growth span made them super awesome soldiers.
After Mace killed Jango, the Kaminoans could only made a few more batches of clones before the sample of his genetic material was rendered useless (something about the process makes it less and less viable as you clone from it).
At the end of the Clone Wars, the clone troopers were reorganized into the stormtrooper corps which were made the elite as they were Jango clones, and Palpatine recognized that he had to make what he had left last for awhile. Around this time there was a clone uprising on Kamino wherein the Kaminoans wanted to separate from the Empire because they were tired of having their services monopolized by Palpatine and used Jango clones to attack the Empire. Palpatine crushed that uprising and destroyed most of Kamino's cloning facilities; this is where the ban on cloning came from, in order to prevent this kind of thing happening again and keep anyone else from creating a clone army to take over the Empire like Palpatine took over the Republic.
A bit later on, the need to begin replacing the fast-dwindling stormtrooper corps became apparent, and so they slowly started to bring in normal recruits, as well as other cloned soldiers from other outstanding Imperial/Republic soldiers using Spaarti technology (which was not as good as the Kaminoan technique due to even more accelerated growth). This replacing caused a lot of animosity between the Jango clones and the new recruits due to the Jango clones' superiority, causing them to look down on the new recruits.
After a time, the 501st was the only pure-clone legion left, which was a point of pride for them. But eventually, even they started to have to bring in other recruits to keep the unit going. By the time of the Battle of Endor, most of the Jango clones had been replaced.