To use GitHub, you'll need to sign up for an account at GitHub's webpage. Accounts are free, and you simply need to provide a username, enter your email address, and click on the "Sign up for GitHub" button.
To download the Github desktop application, go to the GitHub Desktop page and click on the button to download the application for your operating system. You can install the application as you would any other program.
If you are a student, you are also eligible for GitHub's Student Developer Pack, which provides access to a number of different tools and services. Most notably, the Student Developer Pack allows you to have free unlimited private repositories associated with your account ( this feature would otherwise cost $7 per month). To request the pack, go to the GitHub Education page and click on the "GitHub Student Developer Pack" icon and then click on the "Get the pack" button. Note that you need to have already set up your GitHub account to request the Student Developer Pack. You should receive an email when your pack is ready to use.