as far as how they work, well in a word fast.. AK action in a shotgun, there is a gas plug that is marked 1 and 2, some will shoot anything on the #1 setting (lower gas pressure) and some will not..
the plug is intended for the 1 setting for high brass shells, and the 2 setting for low brass
as far as the models, there is a 108, which has the sight rail, the earlier ones did not have a bolt hold open..(it will be by the trigger) the 109 has the rifle sights and most have the bolt hold open.
for the original imports they will be marked European American Armory, current ones Russian American Armory
as far as stocks, the butstock can be swapped with romanian ak stocks, as far as the trigger, it can be swapped with a red star, or tapco g2,
the parts count on them is 14 parts, so if you wanted to go high capacity, or pistol grip, not a lot to change out.. standard mag capacity is 5, but there are mag capacitys of 8,10, and more than that..
generally on break in, they like energetic shells, then see what you can do with birdshot..
as far as cycling, I've had 5 shells in the air at the same time.. there is also a polychoke that you can put on it as well..
prices for new ones are around 500$.. as far as conversion, there are companies that do that as well, or not real hard to do yourself..
as others have said, the saiga forum has a wealth of information.
one of the distributors os local to me, and he tries to keep them in stock, when possible. they are made by Izmash, in Ivshek Russia, same folks that have been making AK's for the russians for years..
only problem I see with them, is it will cause you to look at their other carbines..223,7.62,308....
I like mine..