Because so much of what makes the game enjoyable is discovering these mechanics for yourself, I don't want to get too specific about the puzzle mechanics. I think I can give you a general overview, however.
As each new puzzle mechanic is introduced, the game does a pretty good job of teaching you how that particular mechanic works, all without giving verbal or written instructions. Although the constraints can be fairly easily defined, the puzzles themselves could be quite difficult. Quite often we used pen and paper to figure out how to solve the puzzles.
In addition to having great puzzles, this game is gorgeous. Each environment is beautifully designed and rendered and is a pleasure to look at and explore. Speaking of the environment, I can give you one hint: everything is specifically designed and placed and nothing is random.
We loved this game: really, really, really loved it. If you like solving maze-like puzzles, we highly recommend The Witness to you. Currently it's available for the PS4 and Windows.