There are two main ways to install a WordPress theme: Via the theme section in the WordPress backend or by uploading a ZIP file. This tutorial explains both ways stept by step:
What is covered:
First: Backup
Before you do anything, make sure you backup your WordPress website so you can revert to the current version of your website should something go wrong. With that said, here we go:
How to Upload a WordPress Theme ZIP File

First, go to Appearance / Themes

Next, click on Add New Theme

Then click on Upload Theme

Click on Browse

Pick the ZIP file for the WordPress theme you want to install and click Open

Then click on Install Now

The installer will upload and run the theme installation process. Then you can pick to either have a Live Preview, Activate the theme or to go to the Themes page.

On the Themes page you will then see the uploaded theme available for you to use.
How to Install a Free WordPress Theme from the Backend

On the Themes page, click on Add New Theme

On the right, you can then look for the theme name. I like using Generatepress, so I put that into the text field and click enter.

The theme you search for should show up.

Hover over the theme and click Install.

The system then installs the theme. Once done, you can click on Activate or get a Live Preview.

Like with the uploaded theme, when you go to the Themes page you will then see the newly installed theme there.
And this is it. The main 2 ways to install WordPress themes.