You say you have done some python scripting so you have already started. Look around here, can you provide an answer to any questions that have a python tag? Can you solve other answers with a script? Search blender's api reference to help make your answer. Read other python answers to learn something new. Stuck with something? ask a question and learn from the answer.
The only requirement is a desire to help and some ability to solve problems, even if you don't know how, start searching and experimenting to find the answer. The more you do the more you will know and the quicker you will get at providing solutions.
As you know blender uses python for it's addons, have an idea? make an addon and share it. If it is good enough you may be able to get it included with blender releases. Find other addon projects and see if you can fix any of the bug reports or make improvements, then submit patches to be included. You can find some by searching gihub for blender addon.
Want to help the official blender development? Search blender's bug tracker for addon, UI or python bug reports, note that not all UI and python bugs will be fixed with python, some may need the underlying C/C++ code fixed. If you can fix one then submit a patch to be included. Think an addon can be improved? make the change and submit a patch.
Yes anyone can be a developer, how well you do and how much you contribute to other projects is up to you.