To access the Oxford English Dictionary you will need to authenticate through the UIUC's Duo Factor Authentication system. The preferred browser is Chrome. However, if you have trouble accessing the resource, try a different browser or let us know at email@example.com.
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.