Anonymous Torrent Downloading
I'm not going to ask why you want to download torrents anonymously if you promise not to ask who I talked to and what research I did to come up with this process. I'm also not going to talk about what laws you're breaking or what ethical code you might be violating. And I'm not going to tell you what I think works, but what I've actually tested (for research purposes -- I've actually got no interest in downloading movies myself) here in the US. All good? Great, let's move on.
Low-Cost, But Not Free
This isn't an entirely free anonymous torrent solution. If you're looking for that, you might as well move on. However, this is a low-cost solution and if you're able to pay for the hardware to run all of the fancy software and movies you're downloading, then you're probably able to foot the bill to hide your identity when downloading.
Set Up Anonymous Payment
First off, head over to a grocery or pharmacy and look for the gift card display. I can confirm that Duane Reade has these, but I've seen these displays all over the place. You'll want to grab a Vanilla Visa card. I recommend going for the $25 card to limit your potential losses although the $50 card is more cost-effective since each card, regardless of amount, has a $4.95 activation fee. Pay for this card with cash. You're likely being captured on surveillance cameras, but this is of little concern as it is highly unlikely that anyone organization is going to put boots on the ground to track you down.
Second, take your laptop to an establishment with an open wifi network. Repay this business and get an afternoon pick-me-up by buying a coffee -- I'm partial to iced tea myself. Browse over to https://www.vanillavisa.com/product.html and look for the option to register your card. Use fictitious registration information. However, do use a zip code that's close to the area in which you'll be using your card. I don't know that this actually matters, but since you can you might as well. Also, to make things a bit easier, consider using a new profile in Chrome so that all of your log in information can be remembered.
Now go to everyone's favorite payment processing company, PayPal. Create a new account and connect your visa gift card to the account. Be sure to use the same registration info you provided on the Vanilla Visa site. Also, use a disposable e-mail address.
Off-Shore Torrent Downloading
Next, go to http://dediseedbox.com/ and sign up for their $15 a month package. Provide the same information that you provided to PayPal and pay for 1 month with PayPal. Shortly after payment you'll receive details about how to log in.
It's likely that within hours you'll receive a notification from PayPal that your account has been flagged and that you need to provide additional information to conduct future business. That pretty much does it for this PayPal account so you'll need another one next month. The remaining funds on your card will have to be spent elsewhere -- perhaps for the next coffee you buy where you use the free wifi. This account flagging is also why I recommend the $25 card over the $50 i.e. you won't be able to use the same Visa card number for another account without PayPal noticing.
Downloading the Torrents
I think it's safe to browse the torrent search sites using your own internet access. There's nothing wrong with browsing. While you do this, keep a record of the torrent URLs of interest.
When you're ready to download, connect to whatever open wifi network you can find. Then log into your DediSeedbox account and pop in all of the torrent URLs. Most downloads should finish quickly, but some will take a while. No worries though, just close your browser and let the downloads continue on your server.
The next day reconnect to a free wifi network and then FTP all of the torrents off the server to your machine. For good measure, pause all of the torrents so that they're not seeding (DediSeedbox doesn't really want you to seed and they'll throttle the bandwidth).
When a new payment to DediSeedbox is about to be required, cancel your DediSeedbox account before they try to charge your PayPal account. By doing this you reduce the chances of annoying the DediSeedbox folks. You might as well cancel your PayPal account too. I don't think they actually care about your identity, but rather I'm guessing they're just trying to be compliant with government regulations. Cancelling your account should close the "investigation" so they too should be happy.
Questions You May Have
Am I ripping off PayPal? Nope, they've been paid with the funds you put on the visa gift card.
Am I ripping off DediSeedbox? Nope, you've paid them via PayPal.
Am I getting the owners of the free wifi in trouble? Nope, the fact that their networks are open gives them plausible deniability. And there'll only be an issue if DediSeedbox gives up that person's info which they aren't likely to do given where they're based.
Why don't I just download directly using the open wifi networks I can find? This would work, but there's a very good chance you'll eventually be throttled. Worse yet, because you aren't hiding your tracks the wifi owner may get notified by their ISP to lock down their router which will cut of your access.