If you have Moodle installed on your computer and you want to backup your class and restore on a website host, for example, first it helps to have the same Moodle versions installed in both places (my experience). Do a backup of Moodle in your computer, and note the time because that'll be part of the file name when you look for it later. Then look in your data folder, moodledata, for example, and open it, and you will probably see folders 1 and 2 or possibly more. These numbers represent the classes you've created. Open the folders and look for the backupdata folder and look for the zipped file you just saved in that folder. If you find it, then you know where it's at. Then go to your website host and open Moodle there. Go to "Restore," and follow the path to the zipped file you just found. Upload it to your your Moodle website and restore following the directions on whether you want to restore to a new class or an existing class.
See if that works, and good luck!