There are basically two way to handle the dialogue initiating. You can either load the DialogueData array before each dialogue with JSON (preferably pre-loaded) and then call the "Dialogue_Start()" function with no parameter on any event of your choice. Or, you can use the DialogueDictionary, pre-loaded with JSON data, and use the "Dialogue_Start(key)" function, with key being the name of the dialogue to start, the DialogueData will then automatically be loaded with the data associated to that key from the dictionary.
Here's a very basic screenshot of an example using the DialogueData array.
You should usually pre-load the data though, and store it so you don't have to go through the AJAX routine to start a dialogue. Or simply use the DialogueDictionary method, only one AJAX call is needed in this case.
There are also a few other considerations to have. The default layer for the system is "HUD", so you need a layer with name in your layouts, otherwise nothing will happen. If you have scrolling in your layouts, then the HUD layer should also have correct parallax settings so that dialogue still appear wherever the screen is scrolled to.