To save a graph, first make sure you are signed in to your Desmos account.
A Save button will appear when savable changes have been made to your graph. Click Save to save the graph to your account. If you would like to Rename and Save your graph, click on the title.
Type the name of your graph and press Save.
You'll be able to see your saved graph by clicking the three horizontal lines in the upper left hand corner.
As you make changes to the graph, the Save button will keep appearing. To save any updates or changes, you will need to keep saving.