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torrents are just a bunch of people sending other users the files, rather than one website having to pay for hundreds of gigabytes of bandwidth and hundreds of thousands of dollars of legal fees from copyright infringement
quick and dirty torrent how-to:
1) get a client. I use tixati because it's fast, customizable, and supports rss, you probably won't because it looks like epileptic ass. qbittorrent is good for starters.
2) go to a tracker site. kickasstorrentst/pirate bay/nyaa/whatever. You can look at a list of files you're about to download before you download them
3) grab something that looks cool. for you, this is anime. probably. make sure the number next to "seeders" is high
4) wait for it to download
5) keep the client open so it can seed, open the files like you normally would