I am fairly new to salesforce and I'm having a problem statement which I'm unable to solve.
There is a Custom object named XYZ which has the fields: username, points and Id. Now I want that whenever a particular user points gets updated I get a pop up notification in a visualforce page. I am fairly familiar with the concept of Trigger but I don't know how to use that trigger to update the visualforce page with a pop up notification.
I think you may want to rethink your approach. Triggers are completely data driven, and will perform an action on data within the database, but they aren't going to give you any kind of interaction on the front end save for error messaging.
Your details are a little sketchy, but for the pop-up you probably want to use a Javascript alert, or maybe even some kind of modal window.
If you give more details about the process you're trying to achieve it might be a little easier to give you a more solid response.
