I’m still reading the first book and what I don’t understand is how the shadows are created. Do they work like parallel universes, or are all of them created by the princes of Amber trying to get to a certain place, thus creating some number of permutations along the way?
Shadows are cast by the Pattern (emphasis mine):
...but of Shadow I have this to say: there is Shadow and there is Substance, and this is the root of all things. Of Substance, there is only Amber, the real city, upon the real Earth, which contains everything. Of Shadow, there is an infinitude of things. Every possibility exists somewhere as a Shadow of the real. Amber, by its very existence, has cast such in all directions. And what may one say of it beyond? Shadow extends from Amber to Chaos, and all things are possible within it.
(Page 77, The Chronicles of Amber)
Corwin says that "in a sense" the shadow walkers create them, but personally I think this is him being poetic rather than literal, given the cite above (and given Corwin's penchant for waxing poetical):
You may call them parallel worlds if you wish, alternate universes if you would, the products of a deranged mind if you care to. I call them shadows, as do all who possess the power to walk among them. We select a possibility and we walk until we reach it. So, in a sense, we create it. Let's leave it at that for now.
(Page 123, The Chronicles of Amber)
I think that "parallel universes cast by the pattern" is the truest answer, given:
what we learn about Corwin's pattern, the disruptions to reality it causes, and the null space between patternverses throughout Merlin's books. The role of the pattern(s) in being basic to reality as a foil to chaos supports the stance that the patterns are what "create" the multiple realities called Shadows.