In the left column you'll find various page listings with different databases to help you in your research. Also, note the sword-wielding librarian as well - he's also armed with knowledge (and puns) and can help you find materials and give your research direction!
Related to every aspect of theatre, IIPA is your first best stop for criticism, reviews, theory, and research articles.
Finding plays in print form can be a little tricky - the big problem is that a script is literature, and all literature is grouped together (novels, short stories, poetry, essays, criticism, etc). That's fine if you want to find all of a single author's work together and you're looking for that author. It's a bit more problematic if you want to browse a number of scripts all together.
If you know the name of the playwright, enter that in Search It and that will take you to plays and collections by that playwright - for instance - Neil Simon:
If you don't know a playwright, however, it can be a bit trickier. One useful method is to seek out collections of plays by various authors. Here's a few examples to get you started: