Most databases allow you to limit your search results to "Full Text," meaning results that will be in the database. If you choose not to do this, you will still be able to get to your non-full text results, but there may be an extra step or two.
Limiting to full text will provide results like this:
Otherwise, you may see the "Find it @ CUNY" button next to some of your results. Click this button to explore your options for retrieving this resource.
Clicking the Find it @ CUNY button will lead to a page like this:
If there is a full text link available, click it and you should be all set. If not, you can still retrieve your article via Interlibrary Loan (ILL).