Here are the game download instructions (click on the steps and an image showing more details will be displayed):
Log in to your KSP Store account.
Click the "My Account" button that will pop up after that.
Click the Download button next to Kerbal Space Program in your Products Purchased area.
Select your Operating System and language from the dropdown boxes. After that click the Get Links! button.
Click on the name of the desired version and type. Be sure to read the descriptions and when in doubt just download the recommended items.
IMPORTANT NOTE: After you succesfully install the game, DON'T MOVE ANYTHING, if you move any files or folders out of their default installation directory, the game might malfunction.
If you're having trouble with something not mentioned here, be sure to check the FAQ, or contact us.