The safest place to download Krita is from the project website krita.org. When you visit the download page, you will notice that there are different versions of Krita that you can work with. Each version has a different audience in mind. You will probably want Krita Desktop since that works with desktop and laptop computers. This book contains information up through Krita 2.9.7.3.
Krita.org: The latest news is presented in a blog format. You can subscribe to the mailing list if you’re interested in hearing about new releases.
Make sure to download the correct version for your operating system. If you are on a 64-bit operating system, make sure to download the 64-bit version.
Warning for Mac OSX Users
If you are on Mac OSX, you will find some of the features missing or not working correctly. While Krita works well on Windows and Linux, it is not fully functional on a Macintosh. Even though it is not supported, I have heard good things from the community about it working.
If you are on Windows and download an MSI file, it will have an installer that will guide you through the process. There is also a portable version of Krita that doesn’t need an installer file. This means that there is no installation process. You can navigate to the bin (binary) folder. In this case, you can launch the application by clicking on krita.exe. This is nice if you want to run Krita from a USB stick or otherwise make it portable.