Almost all of the journals for psychology for the last 30 years and older are online. Use Library Search Journals when you know the name of the journal to find out which database provides access to it, or if the library does not have access.
Some current journals and some much older journals are not immediately accessible online, but you are likely to be able to get these through the Library. If you are looking for a particular article in one of these, put in a request to have the article scanned and sent to you through ILLiad.
