To answer the original question,
You basically need to use a VPN or a proxy to hide your IP properly, which essentially are the same thing. Both rely on having access to another computer somewhere in the world, which often requires money... Sure there's the Tor network, which is great, but it's all horrendously slow and using it for P2P is fairly cheeky when people in China are using it to access Google.
VPNs are the most reliable way to securely tunnel ALL traffic through your ISP so that even they don't have a clue what's going on. You can rent VPN accounts for a monthly fee.
The other way is to use a SOCKS or similar proxy. If you're technically inclined these are straightforward to setup. I connect to a SOCKS proxy running on my webserver when I'm uni to allow me to use blocked websites without being caught.
Torrenting over a SOCKS proxy seems a bit hit and miss. Modern torrent clients also use UDP which isn't supported by SOCKS and is therefore sent unencrypted. I don't take the risk of torrenting at uni because they fine people who use P2P. But as a home user it would be an effective way to stop people catching you downloading things illegally.