David Wallace's The Emergent Multiverse is an excellent introduction to the many-worlds interpretation, written by its best defender. Most of it should be accessible to a layperson, although there are technical sections. You can't use it to fully learn quantum mechanics from scratch, though. But if you learn the basic formalism from another textbook (I recommend this one; the first eight chapters should suffice) you'll be able to follow almost all of Wallace.
As for criticism, this is the best non-technical article I know of. It does presume some knowledge of quantum mechanics and many-worlds, but not deep technical knowledge.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one.
3. Open Threads should be posted in Discussion, and not Main.
4. Open Threads should start on Monday, and end on Sunday.