I'm not a lawyer, so don't rely entirely on what I've got to say, but here goes:
Using small portions of a work (a few pages from a novel, paragraphs from a short story, etc.) of a copyrighted work for classroom educational purposes should fall under the concept of "fair use," which means that you don't have to obtain permission from the copyright holder.
However, using large amounts of a single copyrighted work, or, in the case of smaller works such as a particular poem from an anthology, the entire work, is not covered by "fair use."
Keep in mind, though, that for many older works, the work itself might be in the public domain, even if the particular edition of it is not. For cases like this, such as Shakespeare, the way the work is presented (typeface, layout, pagination, etc.) is covered by copyright, even if the words themselves are not.
There's a lot of vagueness in the law, though, so there's room for all kinds of interpretation.
Here are some links that might help:
Fair Use Link
Public Domain Link