Putting your picture on a magazine cover can be done with programs like Photoshop. However, it could take hours and a lot of layer work to make it look right.
Here's a site that does it all for you. It's called MagMyPic. Pick a personal photo and select from dozens of different magazine covers for your photo. It only takes a minute and a couple of mouse clicks to get results like the following. And yes, it's my cat and my son.
And there goes the afternoon.....;-)