I have a C# application, which uses Microsoft UI Automation functionality, e. g. a call like AutomationElement.RootElement.FindFirst(...)
.
Now I need to
As stated in the comments you have to import the UI Automation type library (COM Object) into your project, this can be done with the "Import Component" wizard (Component -> Import Component) in Delphi 2010.
Microsoft kept the COM Object's interface really close to it's .NET counterpart so you shouldn't have much trouble to use it if you are already familiar with the .NET automation library.