BitTorrent is the way to go for P2P sharing. The way it works is this: you download a .torrent file of the thing you wish to download. www.mininova.org is a good site for finding torrents. Then you open the torrent file in a bittorrent client (I suggest utorrent or azureus, just google them). The .torrent file is not the files you wish to download, just a list of trackers and people who are currently downloading/sharing the file.
After opening the torrent file in the client it will start downloading. While you download the file you are also uploading pieces to other people. As long as the torrent is active you can get ultra-fast speeds. You only get a little bit of bandwidth from each person you connect to, but when you connect to hundreds of people it really adds up.
You will have to allow the client access through the firewall, and also may have to forward ports if you use a router. I would suggest using a static IP if behind a router and forwarding ports, otherwise if your IP changes the ports will no longer be forwarded to your computer, and you speeds will take a big hit.
It sounds complicated, but once you get it working it's very fast. And one final warning, whatever you choose to download is on YOU! Don't download any copywrighted or otherwise pirated material!