Study the masthead: Who is the editor? Who’s publishing the magazine? Who is responsible for different sections of the magazine? Can you find out anything about those people or organizations?
Editor: Who was the founding editor of the magazine? Who were the subsequent editors? Are there critical or biographical works on individual editors?
How did the magazine sell itself? Can you find announcements for the magazine in other sources? If the magazine has a website, what does that tell you? Other good sources for this are newspapers and magazines (especially magazines published by the same publisher).
How does the magazine describe itself? Are there editorial columns in the magazine? Editorial columns will often give a narrative of the magazine’s aims. You can also look for memoirs by the editor or interviews.
How did readers respond to the magazine? Does the magazine publish letters to the editor (note that these are bound to be selective)? Can you find reviews of the magazine, or individual issues, in newspapers or other magazines?
Who’s the audience? Sometimes you can find information about audience in secondary sources or directories (see #1 below), or you may have to do some guesswork based on the evidence in the magazine. One important source for this is advertising: what kind of products are being promoted? Who are the likely consumers? What does the advertising copy tell you about who the advertiser (and possibly the magazine) thinks it is addressing?