Find the app labeled "play store" on your device. There you can purchase magazines or subscriptions. There should also be an app labeled "play magazines" that allows you to read any of your purchased magazines.
In addition to Jeffrey's helpful answer, having the kindle app also allows you to digitally subscribe to magazines as well. You would have to sign your android up as a registered Kindle device (from there you can buy books, digitally borrow them from your library as well) and you can purchase kindle edition magazines that are electronically sent to you via the kindle app!