How do I convert a screen position to geographic coordinates?

I'm looking for resources that explain how I should convert screen coordinates (the point that I pick on-screen) to geographic coordinates (lat / lon).

I want to build an application where, the simplified version, I can pick a point from an on-screen map and the geographic coordinates are passed to my database. I have a tile service that serves up raster tiles from a .MBTILES file, generated from OSM data stored in a Postgres databse. The client could be a web application or a WPF (Windows) application.

What are the best practices for doing this?