Helpful article by Shopify on updating themes:
Create a backup of your existing theme. This will be used to copy settings and to keep the live theme running without interruption.
Visit the Shopify Theme Store and log in. For paid themes, it is important to log in to the account that you used to buy the theme. This will prevent you from being asked to buy the theme again. Direct link for the Theme Store for Story:
Click Add latest theme version:
If you see "Try theme" and "Buy theme" options, logout and log-in again with the account that purchased the theme. Be sure the main button has "Add latest theme version".