When you first enter Academic Search Premier, you will see a page with a lot of buttons and search boxes. Don't be overwhelmed. Focus on the search bars at the top of the page:
Enter your search terms on the first search bar and click "Search." You should then see a page that looks similar to this (minus the markings):
In this results page, you can narrow down your search results to items from scholarly journals by clicking the button on the left next to the text "Scholarly (Peer Reviewed) Journals" (indicated by 1).
You can narrow down by date by using the date slider (indicated by 2).
Finally, you can access the full text of articles by clicking "PDF Full Text" or "Check Library for Full Text" links (indicated by 3).
Clicking the title of an article will give you a detailed record with a summary (or abstract) of the article; information on when and where it was published, and who wrote it; and a link to quickly and automatically generate a citation (highlighted):
After clicking cite, you may need to scroll down a tiny way to see the APA-style citation: