Step 1: Download
Download the latest version of QGIS from the QGIS download page
Step 2: Follow the installation instructions
After opening the install package, you will be taken through a prompt. Follow the instructions.
Step 3: Move the application into your Applications folder
After the package installs, move the QGIS application into your applications.
Step 4: Open the QGIS Application
Start by navigate to your Applications folder and double-click on QGIS. You will likely receive an error that says “QGIS can’t be opened because Apple cannot check it for malicious software.” To solve this, go back to your applications and this time instead of double-clicking on the QGIS app, right-click and select “Open.” Then when prompted again, select “Open.” From this point onward, you will not have to go through allowing the software to run every time. You will simply be able to open the app by double-clicking on it.
Launch QGIS. A new project will look like this: