Uploading new files to a Git repository directly through the GitHub web application

Since February 2016, you can add/create/upload new files from the GitHub web interface.

See “Upload files to your repositories “:

You can click the “Upload files” button in the toolbar at the top of the file tree.

Or, you can drag and drop files from your desktop onto the file tree.

This replaces the file creation described in the 2012 answer, and add the upload capability (for one or several files).