It's kind of hard to answer because there are so many possible ways you could decide to start a voice bark. The mechanics for making the text appear can happen in one of two ways that I know of.
1. Osiris call StartVoiceBark(_VoiceBark,_Character);
Where _VoiceBark is the name of a dialog file containing the possible voice barks and _Character is the GUID of the character to do the barking. You can execute this on any event that fits your goals (character enters trigger, character picks something up, character uses something, a timer expires, etc.)
2. Osiris call DisplayText(_Character, _VoiceBark)
Where _Character is the GUID of the character to receive the floating text and _VoiceBark is a string containing the text to display.
It seems like Origins uses methodology #1, so I would try that route. If you open up Origins and just search for that call StartVoiceBark() you'll see tons of examples and then you can unpack the Data\Localization\English.pak file and open up some of the associated dialogues to see how they are structured.
