To participate in the WHATWG and help develop standards and tests, please read the Code of Conduct and Working Mode. Then, sign the Participant Agreement. If you have questions along the way feel free to reach out on IRC or file an issue. The FAQ might also provide some useful guidance. If you want to contribute a new proposal in the space of WHATWG standards, please see this FAQ entry especially.
Once you're all set, you can review the standards and contribute through GitHub as indicated at the top of each standard. You can also help with the development of tests over at web-platform-tests.
If you're just getting started on participating in the WHATWG, we encourage you to check out the global "good first issue" label we use across all of our standards. These are usually refactorings, formatting changes, clarifications, or tightly-scoped bug fixes. They will give you a chance to get used to the tooling and process.
(Looking to update your participant agreement? See these instructions.)