Science is whatever it is that scientists do.
-- the McLean V. Arkansas decision
There might be a million scientists, worldwide. So, they have a social process, whereby ideas spread, and reputations are made. All that stuff on TV is just for the public. Textbooks are for students, and debates are strictly sideshows. Real science is in writing: real scientists publish.
I write my work up as a "paper", and send it to the most impressive publication that I think might take it. If they're serious about their reputation, then they use peer review. That means they ask several experts to review my paper. If the experts don't trash it too badly, the editor sends me their comments, and says that he will publish me if I make some changes. I am not told who the reviewers are, and they may not have been told who I am. (This is for the same reason that we use secret ballots when we vote. It removes any worry about retaliation, or any hope of favor.)
Is peer review perfect? No. I've been on both sides of the process, and, well, it's a process done by humans. But it's really pretty good, and I don't know of anything better. Peer review tends to create high standards. Most scientists, myself included, have had a paper rejected. The usual response is to improve the paper and submit it to another journal - perhaps a less prestigious one. Weak or sleazy science is mostly pushed all the way down the food chain to the really minor journals, to books, and to NBC and Leonard Nimoy.
Occasionally there's a fuss. A journal may publish a rebuttal article. There have been small wars. where one journal published articles on one side, and another journal published the other side. An author who can't get published may found his own journal. If the new journal becomes prestigious, then presumably he was justified.