The following demo shows how to use create a new item using REST. It will really add data to the database.
This uses AngularJS and will use $http to do the ajax and will add the returned items to the ol-tags.
Note that we recommend using the content service, but this is to demonstrate absolute basics
Note that it works for admins by default - to make it work for visitors you have to allow create-permissions for anonymous users (or users with view permissions). This is configured on the content-types - for more infos read Permissions Help.