I recently finished reading The Articulate Mammal by Jean Aitchison, which is an introduction to psycholinguistics; and I liked it a lot. It deals with the three basic questions of psycholinguistics:
And it does so in a very accessible style. Although it is not a popular science book, I believe it can be read by non-linguists or non-psychologists without a lot of difficulty.
Its only weakness is that it focuses mainly on Chomsky's theories; other ideas are only mentioned as far as they criticise Chomsky, and are not laid out in as much detail. It does give a good overview, though, and there are suggestions for further reading for every chapter, which, together, makes it a great introduction.
I especially recommend it to beginning students of linguistics. When I took an “Introduction to Linguistics” class we had to learn X-Bar syntax without anyone telling us why one would think of syntactic structures as trees, we only learned how to construct those trees. Or the idea of the mental lexicon: it just came up at some point, but again, no one ever explained why it was thought of in that way. I think some basic psycholinguistics should even be mandatory – or integrated into linguistics introductions. So if you are a student of linguistics and didnt't get the chance to visit a psycholinguistics course, I urge you to at least read this book.