JMP exposes its functionality via OLE automation which means that you can access JMP functionality via languages such as Visual Basic or C#.
If you look in the installation directory of JMP you will find a PDF document called Automation Reference that defines the object model and method calls. There is also a directory containing sample code.
You say that you are a beginner with web services -so your first step is to learn how to implement a web service using your preferred .NET language.
You can then simply insert JMP object method calls into your web service definition.