GOG Galaxy offers cloud saves as an optional feature for some specific games. The cloud save feature can be enabled or disabled in the settings for Galaxy, which you can access by clicking on the GOG.com logo in the top left corner of the client.
You can see the complete list of games which support cloud saves by searching our catalogue for the cloud saving feature. A game that supports cloud saves also has a "cloud saves" tag in the features list of its store page.
To upload your saves to the cloud, all you need to do is start the game via Galaxy; if it supports cloud saves and you have enabled the feature, your local saves will automatically be synchronized with the cloud. Your saves are also synchronized after you exit the game, as long as Galaxy is still running in the background.
If you want to download a backup copy of your cloud saves, please open the library entry of the game in question, click on "More" and choose "Backups & Goodies" in the dropdown menu. The cloud saves are available under "Cloud Saves Backup Copy".