This is a bit borderline, so don't drop anymore details on what you want to do here.
Keep in mind that what they are doing might upset you, but it's not illegal. What you are wanting to do, that is.
i.e. Some racist white person may want to remove all black people from facebook and try to hack it to get the owner to rethink allowing only certain races to join the site. I know this seems a bit far fetched but it's the same concept.
To answer your question, to bring down a website, you can use DDoS attacks. I suggest you google this and look into it, as I will not explain any methods of how to do this, simply because of the nature of the post.
I can't help you fully here, but best of luck,
Spreading knowledge just once a day, can help keep the script kiddies away ⠠⠵
The mystery is intensified by the facts.