The Corona SDK framework is a commercial tool, but they have a completely FREE version available. You can even use it to publish a finished game to the App Store for free or paid. So you can do the entire development process without paying a dime, and even make money with it without paying a dime, which makes it an awesome choice for learning.
Look for the download link for Corona SDK at the Corona Labs site:
After you download the file you'll have to install it. If installing software is something you can do in your sleep, just go for it -- there's nothing special about the Corona SDK installation process.
If you need more guidance, see the following pages for step-by-step instructions:
To Install the Windows version of Corona SDK:
To Install the Mac version of Corona SDK:
That should get you ready for the next step, installing the IDE (Integrated Development Environment) called Outlaw.