Client side databases are limited to the website and the client. This means you won't be able to do any type of data transfers to where if you're wishing to share one client's data with another without going to some form of server side scripting.
If you are JUST going to save data between the user and the webpage, and nothing more, you can save data using JavaScript in cookie forms, or using the browsers build in localStorage method. Either way, both methods are limited in the amount of memory you can save. A quota if you will.
LocalStorage uses three methods in JavaScript.
window.localStorage.getItem(key);
window.localStorage.removeItem(key);
window.localStorage.setItem(key, value);
The function names are self explanatory.
getItem finds the key specified and returns it's value. If the key is not found, it returns undefined. removeItem removes the key specified from the user's localStorage. The setItem sets the key with the proper value sent, in the users localStorage. The localStorage is also treated as a JavaScript object, thus, window.localStorage.getItem(key) is the same as window.localStorage.key. window.localStorage.setItem(key, value), is the same as window.localStorage.key = value, and so on. Using the functions are just a more conventional method of using the localStorage object.