If you followed the tutorial for installing WordPress plugins, you will already have the skills needed.
When you download a theme, you'll find that it unzips into its own folder. The following template I downloaded and unzipped is called Andreas01. You'll see that the theme includes two folders, wp-andreas01 which contains template files, and the img folder inside that one that contains images for this template.
Open Filezilla, and connect to your domain space where WordPress is installed.
Once you are logged in, double click the folder on your server called “wp-content” .
Inside that folder you'll find several others. Double click on the one called “themes“.
Inside this folder, you'll find some other folder. Each one of these represents one theme already installed. In the screenshot below, you'll see the two that are installed by default when you install WordPress.
Simply left click the downloaded theme on your hard disk (click the folder wp-andreas01 in this case), and hold the mouse button down. Drag the folder over to the right hand side of the screen, and drop it somewhere on the white background of your server space:
The folder will be copied across to your server.
Next, login to your WordPress Dashboard. Click on the Design -> themes menu item.
On the theme screen, scroll down to the “Available Themes” section. You will see your new theme. Click on it.
The new theme will then become the Current Theme (you'll now see it at the top of the page listed as Current Theme).
Go and view your site now, and it will be using the new theme.