As you do your research, you will move back and forth between the primary and secondary texts. But let’s take them separately, here.
You will need an archive of primary materials—copies of the magazine you are studying.
You may find print versions of these in the library, online, or on microfilm. Use the “Finding Magazines” folder (on ctools, in the Resources tool, inside the Library Resources folder.)
One basic distinction here will be between working on historical magazines and on contemporary magazines. Some magazines have a long history and are still being published, so you will work with both—but they will present different challenges.
You will need to use a wide array of secondary materials to support your research. Those are infinitely varied—what kinds of materials you need and what’s available will vary depending on your topic.
For a historical magazine—look it up in Frank Luther Mott’s History of American Magazines (available in print and electronically), which covers those founded before 1930. There’s an index in each of the five volumes, but you’ll want to use the index to the whole in the last. If he has done a “sketch” of your magazine you have your starting point. If not, search out the references. You might also try John Tebbel and Mary Ellen Zuckerman’s The Magazine in America 1741-1990, which is less thorough but covers an important additional 60 years. Both will provide also helpful information about where your magazine fits in the industry—it’s good to know about its competitors, other magazines produced by the same publisher, and so on.
There are no equally authoritative starting points for a contemporary magazine.
The magazine itself will provide some information—look in the magazine itself, and on its website. There may or may not be some history; there will almost certainly be a ‘media kit’ with very useful information. Remember that the magazine is selling itself there—don’t rely on the information uncritically.
Next, check Ulrichsweb Global Serials Directory for basic information about the magazine, including editors, audience, and circulation.
There is nothing wrong with using Wikipedia. But remember—this is a starting point. Wikipedia’s rule is that it does not give any original information but always points to other sources; follow on to the material mentioned in the sources or simply use the entry to orient yourself in your search for secondary sources.
There may well be useful information for you in general-interest books and journalism.
You will want to find, read, and cite scholarly works—both books and journal articles.
As your analysis progresses, and especially as you move towards your term paper, you will need multiple kinds of secondary sources. Some of them may not be about magazines at all.
Be sure to keep track of your sources, even at the beginning of your work; you’ll need to be able to cite them.