[angularjs] How to reload / refresh model data from the server programmatically?

You're half way there on your own. To implement a refresh, you'd just wrap what you already have in a function on the scope:

function PersonListCtrl($scope, $http) {
  $scope.loadData = function () {
     $http.get('/persons').success(function(data) {
       $scope.persons = data;
     });
  };

  //initial load
  $scope.loadData();
}

then in your markup

<div ng-controller="PersonListCtrl">
    <ul>
        <li ng-repeat="person in persons">
            Name: {{person.name}}, Age {{person.age}}
        </li>
    </ul>
   <button ng-click="loadData()">Refresh</button>
</div>

As far as "accessing your model", all you'd need to do is access that $scope.persons array in your controller:

for example (just puedo code) in your controller:

$scope.addPerson = function() {
     $scope.persons.push({ name: 'Test Monkey' });
};

Then you could use that in your view or whatever you'd want to do.