I just enabled Steam Cloud Saves. All of your save files will be synchronized between your different installations. If you already have the game installed on multiple machines, please run the game on the machine with your most recent saves first to synchronize those save files to the cloud. When you run the game on a second machine you will be asked which saves you want to keep.

If you would like to backup your saves independently, they exist in the game's install directory and have a .sav extension.

The next update will have an improved Saves window that includes delete with confirmation.