A magazine is usually what the U.S. Copyright Office calls a "collective work." This means it's a single editor's vision but a collection of works from many contributors. In some cases, small hobby newsletters for example, the magazine may be entirely one artist's creation. The person seeking to copyright the magazine may not be a natural person. It may be a corporate entity. Ultimately, none of that matters much. The process to copyright a magazine is similar whether it's created by one guy in his basement or by an international conglomerate using contributors from all over the world.
Create or commission the articles and artwork for your magazine. No one can copyright ideas or concepts. You can only copyright the actual ("fixed'") expression of your idea. So, to copyright your magazine, you must first create an issue as the fixed expression of your idea of the magazine.
Contract with your contributors for the copyright of the materials that they create. Creators generally own the copyright of their work. You have two important exceptions. First, you own the copyright in works your employees create. You should still have them sign a contract assigning you the copyright, but you'll still be on pretty solid legal ground without one. Second, you also own the copyright to works that you hire people to create if you have a contract stating their work is made for hire. You must have your freelance contributors sign a "work for hire" contract giving you the right to copyright their work in your magazine.
Edit the issue of your magazine into its final form. In fact, once you have created or collected your articles and artwork and signed the contracts you own the copyright to all the information in your magazine. You automatically get a copyright once you have fixed your idea in a particular creative expression. But you will want to register your magazine to get some additional legal remedies if someone uses your magazine improperly.
Register your full final edited magazine with the U.S. Copyright Office. To register you must file an application form, a non-refundable filing fee and a copy of your final edited magazine without the advertisements. You don't own the copyright in the advertisements. Those belong to the merchants. When you register your magazine, you get a public record of your copyright claim and presumptive evidence in any lawsuit that you own the copyright. You also have to register your copyright before you can sue someone for using your material improperly.
Deposit two copies of your magazine with the U.S. Copyright Office within three months of publishing it. You have to do this whether or not you register. If you don't, it won't affect your copyright protection but you may have to pay fines and penalties.
You may choose to record copies of your work for hire contracts with the U.S.Copyright Office. You don't have to. But if you do, you'll have a public record of the contracts in case you later have a dispute with one of the creators.
You now own the copyright of your magazine for 95 years from the year you first published it or for 120 years after you created it, whichever is shorter.