GameMaker: Studio is available for download exclusively for Microsoft Windows at http://yoyogames.com/studio. There are a few different versions available, each adding more functionality as the price point increases. All of the versions allow you to create games using the game engine. For the most part, the increased functionality relates to publishing your game to different platforms as well as providing some additional features.

The Standard Edition is fully functioning and is perfectly adequate for developing games in GameMaker: Studio. The Professional Edition includes many more features than the Standard, such as team features, early access builds, the ability to purchase additional export modules, and allows the developer to publish games to platforms beyond Windows and GameMaker: Player. The Master Collection contains everything available, which is the Professional Edition bundled with all the export modules. The additional export modules cannot be purchased with only the Standard Edition of GameMaker: Studio.

Whatever version you choose, keep in mind its limitations and what you might need, but do not pay for more than you need. You might purchase the Master Collection and end up only using the additional HTML5 module, making the additional features unnecessary. However, keep in mind that you can commercially publish your games with any version of the IDE, but the Standard Edition will force a splash screen and application name that both say "Made with GameMaker: Studio".

You can always upgrade later, so the Standard version is a perfectly appropriate place to start. Once you've chosen your version, get a license key for it and download the GameMaker: Studio installer and run it.