Take the controller apart and see what is causing the issue. Clean out any debris or liquid, sometimes people get liquid inside without knowing it. Spray from opening a can of soda or Monster type drinks can get inside these joints and cause them to be sticky.
Once the controller is apart, clean the button and all the plastic casing around it. After the make sure the button works mechanically and that it is able to be depressed. If not you may be able to see what the problem is.
Guide: [guide|36558|Xbox One Controller Trigger Replacement]