I need to select a block in AutoCAD, and move it up or down vertically. I can get to the point where I have the user select a particular block, but after that, how do I get a reference to the block selected so I can move it up or down?
If you're new to AutoCAD .NET programming, you should download the labs, and other learning materials available and go through them. What you're asking is very basic stuff that you need to know before you actually try to write applications or plugins with .NET. Going through the learning materials, labs, and samples will answer your specific question.
Once you get the user's selection (an ObjectId), you have to start a transaction, and then use the transaction to open the selected object, using the ObjectId, which is accessed through the PromptEntityResult object returned by the Editor's GetEntity() method.