You can access the OED Online by going through the Library Gateway: http://www.library.illinois.edu/: simply type "OED" into the Easy Search box and hit Go, then select the direct link to Oxford English Dictionary at the top of the results screen. (Note: if you're off campus when accessing OED Online, you'll need to log in with your NetID and password.)
Use the search box on the front page of OED Online to enter your search term(s):
Click "Go" and a new window will bring up your results (click on image for larger view):
From this page you can select the specific word you're looking for. As you can see, the results page offers concise excerpts from full definitions that can help you narrow down your search and find the entry you're looking for. Additionally, the letter after the word on this page will indicate the part of speech described in the entry: "alphabet, n." will bring up the word's usage as a noun, while "alphabet, v." will bring up the word's usage as a verb.
An index of common abbreviations used by OED Online is available at http://www.oed.com/public/abbreviations. This can be helpful when looking at words' origins and histories.
Unlike the print edition, the online edition is updated quarterly (most recently in December 2012). You can find an index of the most recent additions to the OED Online (such as "state-dependent," "senioritis," and "Long Island ice tea") here.