In AngularJs all the scopes are bound to DOM so to access $scope first we have to get the HTML element. You can either use jQuery selectors to get elements or you can use standard document.getElementById method. For example.
var scope= angular.element($(".classselector")).scope();
This gives you the scope of the the element. Once you have the scope you can call respective method of controller. There is also other way to find out the scope if you don't have reference to element. You can find scope by name of controller.
var scope = angular.element($('[ng-controller=myController]')).scope();
After you make changes to variables of scope you have to call apply method so the AngularJs framework is notified about changes.
Hope this helps you.