Measurements, Reference Photographs, and Notes
I start a repair by sketching things on paper, trying to identify the most important features. I take measurements with my calipers and annotate the sketch. This is usually enough detail to create a replica of something "blocky" like a bracket or simple lid.
Sometimes the thing I need to replace doesn't have just a few straight lines that can be easily replicated or measured (as with the plastic play structure horn cap or bud vase). When that happens, I use reference photographs - sometimes with a common object for scale (such as the quarter used in the fairy wing replacement).
The photographs are best taken with the object against a contrasting background (either very dark or very light).