This post is about accessing SSAS using Visio 2010.  For a great article on SSAS & Visio 2007, check out Dinesh Asanka's article here.

Some of the menu options are different between Visio 2010 and it's predecessor Visio 2007.  In Visio 2007 there was a Pivot Diagram option in the Data menu that would allow you to use Analysis Services as the data source.  As far as I can tell, Pivot Diagram has been removed from the Data menu in Visio 2010.  Of course you can still use the Pivot Diagram feature in Visio 2010, but it involves using the Shapes menu. 

Just create a Visio document and open the shapes menu. 

Then using the shapes menu browse to: More Shapes -> Business -> Pivot Diagram -> Pivot Diagram Shapes.

In the Pivot Diagram Shapes menu, there is a shape called "Pivot Node".

After dragging the Pivot Node shape on to the sheet, you will be presented with the Data Selector wizard, which allows you to select Analysis Services as an option.

Complete the wizard and connect to SSAS, just like you would in Visio 2007. 

From this point on, everything you know about working with Pivot Diagrams from Visio 2007 carries over to Visio 2010.

Enjoy!