There are so many ways to implement a dialog system.
At the simplest level you need to:
1) Trigger the conversation by some event, like clicking on a sprite or one object colliding with another.
2) In response to the event, use the set text action of a text object to set the text to the desired text.
This simple project shows a sprite saying different things when it collides with another sprite.
If you want something more involved, my "port" of Mikey's adventure part 2 also has a little bit of dialogs. For example, here is the section dealing with Mikey's conversation with an NPC called Jill. Maybe not the best model to copy, but hey, it was a learning experience!
<img src="https://dl.dropbox.com/u/57899112/MikeyTalksToJill.PNG" border="0">
There are also links to several threads in kyatric's (How Do I...) Frequently Asked Questions thread. under the RPG genre section that discuss a more full fledged dialog system.