Here's the form: https://www.youtube.com/copyright_complaint_form
Click "copyright infringement" and "infringing on me", add the target video's URL and it will be taken down automatically. It won't be restored until the appeal process is finished (usually several months).
While most of the content on YouTube is just "random junk" the most watched / popular content belongs to large networks, large networks work with YouTube through their content ID program which is treated slightly differently when it comes to DMCA claims.
Things get slightly more tricky because videos can have Multiple content ID's tagged to them by YouTube so if you upload a video with various music clips one owner can decide to mute it while another decides to block it completely.
That said if you are an original content creator once you've submitted content to YT's content ID program and you prove that you own exclusive rights for that content it pretty much protects you from the normal DMCA process.
There are few enough (more than 100, less than 1000) major YouTube distributors that YouTube just manages the relationships individually. This is often cited as a perk of joining a distribution company - they have greater clout in resolving disputes with YouTube because they have access via back channels due to representing so many content creators.
The entire abuse process on YouTube is far more manual and bureaucratic than most people on the Internet seem to think.
So what could YouTube possibly do to you for misusing the process? It's not a federal legal thing anymore. I suppose the takedown-ee could sue you for missed revenues if they really wanted to, but seeing as how there's nothing preventing bogus-named accounts from filing takedowns....