How to clone a git project from the website to your desktop?

You need to be logged into the website (GitHub.com) and the application and refresh the page. Then you can click clone to desktop.

You could also install command-line tools. From the app, Preferences > Advanced > Install Command Line Tools

The GitHub functionality to 'Clone in Desktop' has been replaced by a drag and drop feature which is not quite clear. The process to do this is explained here: http://joe.blog.freemansoft.com/2014/04/github-clone-to-desktop-with-windows.html

They've changed the button now to this tiny one to the right of the url:

Clicking on it opens the desktop app if you've installed it