There is 2 ways of doing that. One is by uploading a theme on WordPress panel, and the other one is by uploading a theme through FTP.
Install through WordPress panel
First you need to have a theme file downloaded on your computer and compacted as zip file.
E.g.: the Simples theme has a file simples.zip
After you have a theme file in zip format, log in to your WordPress panel and go to Appearance and then click on Add New, and on the next page click on Upload Theme.
On the next page, click on the button to upload the theme file.
After that, just go to Appearance and click on Install that show up on the theme you just installed.
To install a Child Theme is the same thing.
Install through FTP
After you bought a theme, unzipped it first. It doesn’t work if it is a zip file, you need to unzipped it.
E.g.: the Simples theme has a file simples.zip that when you unzipped, it just a directory called simples.
You will need to have a FTP program installed on your computer.
After that, log in with your site FTP access on the program.
Then go to directory wp-content/themes/ and upload the theme you just unzipped.
If you don’t know how to use a FTP program, we recommend you install the theme through WordPress panel.
On the blog we have a tutorial on how to use FileZilla (portugues only).