A computer joins a BitTorrent swarm by uploading a Torrent file into a BitTorrent client. There is a server called as a Tracker that is used for sharing the IP addresses of all the connected clients to the other peers. Once connected the bittorrent files would be downloaded in pieces and once there is some data then it can upload the data to the bittorrent clients in the swarm. In this way everyone who is downloading a file is also uploading a file and hence the speed increases.
Leechers and Seeders: Users downloading from a bittorrent swarm are called as Leechers or peers. Once they have downloaded, now then can help in the upload bandwidth by becoming the seeders. For a torrent to be downloadable one seeder who has the complete copy should join the swarm.