Can I make a game so that it saves user data as he plays? and he can load that data?
What Language are you using.
If you're using Python or Lua then no. (Not without Modules)
Here's more info about Local Storage (Web Storage) : https://www.w3schools.com/html/html5_webstorage.asp
Here's a good wrapper for local storage : https://github.com/andris9/jStorage/blob/master/README.md