You should start working on a project on GitHub by using the below-mentioned ways:-
1. Firstly, choose the language/technology that you would want to work on this is the most import part while you start using GitHub.
2. Choose a project which uses that language and start doing it.
3. Look for any bug/enhancement from the available list.
4. Setup the development environment. You may fail. Keep trying until you set it up successfully
5. Try fixing the bug. You will fail for sure. Keep trying it until bug gives up.
6. Raise a PR. There are more chances that it might get rejected.
7. Address the review comments. Never give up until you get your changes in.
By this time you either lose interest or get addicted. Either way the learning which you got from step #4 - #7 is something which you cannot get unless you contribute to open source project in GitHub.
Some of these learnings are
How to fix a product without breaking it
How not to code
How not to design
How the experts think and approach in solving a problem.
How would it be to work on a large scale product (if you had chosen to work on an enterprise-class product)
If you are a beginner to the GitHub you should learn it immediately as the need arises to learn GitHub in detail which is necessary for a programmer you can learn it by taking up the GitHub training course. If you like to read then you can have a look at the GitHub tutorial. If you want to learn it by watching the video tutorial then you can have a look at the following tutorial:-