I think the mechanics of how to actually take down content is getting pretty far past my knowledge but I suspect this falls in the general category of "people still have the free will to break the law" and isn't about copyright law particularly. The takedown process is specific to the DMCA's concept of online service providers - YouTube keeps its safe harbor as long as it promptly responds to takedown notices (and counternotices). But if you want some content off my personal blog, there isn't a specific "takedown" procedure - you just tell me that every time someone downloads it, I'm making yet another illegal copy, so it's probably a good idea for me to get rid of the page. If I refuse, I think your legal process is roughly the same as if I were defaming you or whatever on my blog.

https://www.law.cornell.edu/uscode/text/17/504 has some details on damages (but also note https://www.law.cornell.edu/uscode/text/17/412 , that you need to register copyright to get the option of statutory damages). I think (but I am a bit unsure about this) that if I posted some copyrighted content on a blog without permission, I'd be liable for the $750 in damages if the copyright holder had registered it and found it worthwhile to go to court to get it.