DSO stands for Microsoft Decision Support Objects and is an object-model for managing the Analysis Services environment. Anything you can do through Analysis Manager you can programmatically do with DSO. To use DSO, you have to write code in a development environment that supports COM, for example, Visual Basic, Visual Basic for Applications, Windows Scripting Host, ASP, .NET, etc. Add a reference to the Microsoft Decision Support Objects library in your development environment and start coding. A lot of information on the object model can be found in Books Online or MSDN.
DSO is not how you query a cube, however. You will need to use ADOMD (another COM object library) or XMLA. These technologies allow you to access the data in the cubes programmatically. Again, a lot of info online how to use ADOMD and XMLA.
I am not familiar with mining models, so I cannot offer any help there.