The first thing you'll need to learn Salesforce DX is a free Salesforce Developer account, which you can sign up for here:
https://developer.salesforce.com/signup
In this video, you'll learn how to set up Devhub and give users Salesforce DX access.
Anthony walks you through the process of installing the Salesforce CLI in this lesson.
Refer to the Salesforce DX Setup Guide section for installing the Salesforce CLI here:
https://developer.salesforce.com/docs/atlas.en-us.sfdx_setup.meta/sfdx_setup/sfdx_setup_install_cli.htm
In this lesson, Anthony walks you through installing Visual Studio Code.
Go to https://code.visualstudio.com/ for the latest version of Visual Studio Code that you can install on your own computer.