The Office team has put up video of all of the presentations from the Office Developer Conference held this past spring. At the conference, I presented a Visio 2007 session focusing on building solutions using the new Data APIs. The direct link to the video of the session is available here. The quality of the video is high, so beware that it is a 182 MB download.
In the session we cover the three main aspects of programming against the Data APIs: Importing the data, linking the data to shapes, and displaying the data using Data Graphics. Along with the slides detailing the APIs and some possible scenarios, I build an example application (visualizing sales on a supermarket floor plan) from scratch.
Here's a high level guide to what is in the presentation:
We'll be publishing full documentation on the Data API soon, but this should give you a good introduction to what is possible and some tips on how to get started.