Download the class private key. It was probably emailed to you as a file named classes. For Windows, you need classes.ppk, which is the same key in a different format. For Mac and Linux, you need the key to be readable only by your user account. You can do that on Mac by right clicking on the file, clicking Get Info, going to Sharing and Permissions at the bottom, and changing the permissions accordingly. On Ubuntu you can similarly right click, click Properties, then click Permissions and change them. Or you can run chmod 700 classes from a terminal.
Download TortoiseHg. For Windows or Mac, download it from their website. For Mac, you can also install using Homebrew or MacPorts, but it might be more painful (see here). For Ubuntu, you can get TortoiseHg from apt (sudo apt-get install tortoisehg tortoisehg-nautilus). Older versions may need to first set up a PPA (see Sam’s tutorial here).
Start TortoiseHg and open the global settings menu. On Windows, right click on the Desktop or Windows Explorer, click TortoiseHg, then click Global Settings. On Mac, start TortoiseHg, then click TortoiseHg at the top left and click Preferences. On Ubuntu, run TortoiseHg from the application menu, click File at the top left, then Settings.
Change TortoiseHg settings. Under Commit, enter Username formatted as Your Name <email@example.com>. Under Sync, put ssh -i /Users/YOUR_NAME/Downloads/classes for Mac or Linux and TortoisePlink.exe -ssh -2 -i "C:\Users\YOUR_NAME\Downloads\classes.ppk" for Windows. Make sure to specify the correct path to the key file (substitute YOUR_NAME to make the right path).
Clone the repository. From TortoiseHg Workbench, click File then Clone Repository. For Source, put ssh://firstname.lastname@example.org:846/863.14. For Destination, put a location on your computer (e.g. /Users/YOUR_NAME/Desktop/864.14). Click Clone.
Use the repository. You can commit, pull, and push using the TortoiseHg workbench or integrated file browser hooks in Windows or Ubuntu. Consider reading a more extensive tutorial on Mercurial to understand exactly what’s happening (maybe Sam’s tutorial, Charles’s tutorial, Neil’s page, or hginit.com).