To save a map click on the Save As button at the bottom of your map page. Add your property/project's information and hit Save. You can also do a quick save by just clicking the Save button next to the Save As button.
Tip: Only use the Save As button for your initial save and for anytime you need to edit your map details such as Highlights. The Save button is a much faster way to save when just editing the map.
See video below for a visual example.