In a novel that I am reading, the following quotation appears: ?How
sweetly on the hill-side sleeps [/] The sunlight with its quickening
rays! [/] The verdant trees that crown the steeps, [/] Grow greener in
its quivering blaze.? I would like the name of the author, and the
name of poem or work from which it comes. If you can give line
references (with stanza or act number, etc) and the page number to an
edition with the details of the edition, including editor, publisher,
place of publication and date, that would be very helpful.

This appears to be a quote from "Clotel; or The President's Daughter",
by William Wells Brown.

It comes from Chapter IV, entitled 'THE QUADROON'S HOME'. 

The actual quotation you have given is actually at the very beginning
of Chapter IV, and so it follows that "How sweetly on the hill-side
sleeps" is actually line one, and so on.

http://www.knowledgerush.com/paginated/clotl10a/clotl10a_s5_p1_pages.html
http://www.sourcecentral.com/library/39-1.html

There are numerous full versions of this text available online. One of
which is the project guttenberg text available here:

http://www.gutenberg.net/etext00/clotl10a.txt

I'm not a google researcher, so this is all the information I'm gonna
give you for now. For future reference, you should know that finding
sources of quotes is extremelly easy with google. Simply take a line
from the quotation you are researching, be sure to include it in
quotation marks, and click search.

I slipped the following into google:  "How sweetly on the hill-side sleeps"

Try putting that into the google search engine complete with quotation marks. 

Hope this helps,

Paul