I made a QuickPart to Normal.dotm and now I want to place it to the document
(where the cursor is) using C# interop. The basics (create application, create document, locate cursor etc.) doesn't need to be covered, I know those, but how does the beef of that work like?

Here's the same as "pseudocode"
Word.Document ActiveDoc = Globals.ThisAddIn.Application.ActiveDocument;
Word.Selection selected = Globals.ThisAddIn.Application.Selection;
Word.Range rng = selected.Range;
rng.AddQuickPart("Normal.dotm", "ThePartIJustCreated"); //This one obviously doesn't work