You need to be comfortable with Python language, which you can learn in a few days from tutorials on the web. Then the rest is about getting to know libraries. Slicer mainly relies on VTK (that you can learn from VTK textbook and examples), ITK (for image processing, that you can learn from the ITK software guide), and Qt (for GUI; which you can learn from Qt documentation and examples). Slicer adds a little extra layer and logic, which you can learn from studying Slicer programming tutorials, script repository, and source code of Slicer core and extensions.
The tutorial that I linked above is a good starting point and you can always ask questions here. You can also come to one of the Slicer project weeks where you bring your own problem that you work on with help from Slicer experts.