I want to learn how to program improvements for Musescore. Where do I start?

Javascript:
MuseScore plugins are written in a form of javascript. Any beginner's introduction to javascript (plenty on the web) should suffice (see Plugin development handbook for details). Plugins allow you to work will small amounts of code and improve MuseScore in limited ways.

C++:
MuseScore's actual software is written in C++ which is an more sophisticated language but older and more difficult to learn. There are more things that can go wrong in C++, and the code requires compilation before it will run (which slows things down for the programmer).

You:
Think about what you are already good at and ways that you can use those skills to help MuseScore. Programming is just one of many ways you can help MuseScore. I encourage you to start with something relatively simple for you. There will be plenty of opportunities to grow and learn from there. On the other hand, don't feel like you need to understand everything before you start a project.