I was asked how one contributes to standards. Before anything else, it is worth watching Domenic Denicola’s presentation on making friends and influencing standards bodies. It is awesome and will teach you a great deal.
I think the core thing to understand when considering contributing to web standards is that they are created by communities. Typically there are a few people leading the charge and many people contributing with critique, research, and tests. Usually there is a combination of mailing lists, IRC, and the occasional face-to-face meeting, to keep everyone roughly synchronized.
You want to figure out what community to participate in:
Unfortunately there’s a myriad of other smaller lists for particular APIs. Usually the standard you care about has relevant pointers. If it doesn’t, please file a bug or let someone else know as it definitely should.
Studying the output of the community (the standard and tests) and its ongoing progress (the mailing list) is a good way to get a feel for how things work and what you should pay attention to. It can help to read the WHATWG FAQ too as it documents answers to many common questions. Having familiarized yourself with the material and the environment you should feel more than ready to start participating more actively, in particularly if you see something worthy of improvement.