After you've found the publication you're interested in, simply follow the links to the website for the time range of interest. (Note that many online subscriptions are limited to a range of years and there are often different sources for different time ranges.) If you're on campus, you typically will not have to log in with your NetID. You can then bookmark the website for direct access next time. Once you are within the journal's website you can usually search for an article by year, volume, author and keyword. Most subscriptions also allow you to view and download a pdf version of the article.
As a UIC student or faculty member, you can also access online subscriptions from off-campus. The easiest way to do this is to follow the same instructions above. After clicking on the link to the journal from within the UIC library website, you will be asked to enter your UIC NetID and password. This process will connect you to UIC's proxy server so that the journal's website will "see" you as connecting from the UIC campus. Voila! The key here is you must go through the UIC library website each time. If you do a lot of online research, this becomes tedious. An alternative is to add ".proxy.cc.uic.edu" to the end of any restricted website's URL. For example, the URL for The Journal of Organic Chemistry (JOC) is:
Since I already know that UIC has a subscription to JOC, I just enter the following into my browser's URL bar:
Notice the ".proxy.cc.uic.edu" is entered right after the domain name (e.g., .org or .com), not at the end of the URL. An advantage of this method is that you can bookmark the proxy URL on your off-campus devices so that you don't have to go through the library website or enter the ".proxy.cc.uic.edu" each time. This method will only work, however, if UIC has a valid subscription for the site you're trying to access.