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.