Let's get this straight, there is NO way to prevent yourself from being tracked, but these methods should protect you from most anti-piracy organizations as most don't have the legal/technical infrastructure to pursue past things such as VPNs.
A VPN, or a Virtual Private Network, is a way of cloaking your IP and encrypting all of your internet traffic so your Internet Service Provider and snoopers at coffeeshops can't see what you do online.
Many people regard VPNs as an excellent, and easy way of protecting yourself, especially on public trackers such as 1337x, The Pirate Bay and RarBG. In some cases, they also allow you to bypass ISP throttling for torrents.
While getting a VPN subscription, you should check for if the service:
Does NOT keep logs for any of the user activities.
DMCA notices are handled if your favour.
Their physical servers are located in countries that compliment piracy.
Generally, you wanna select a server from a country with no copyright laws or the ones who don't care.
A list of countries without or "inactive" copyright laws:
Some countries where piracy is on a wide enough scale don't care either. Generally countries such as China, India and United Arab Emirates.
Here's a short list of VPN providers who "claim" to abide by these statements.
You can also run your own VPN for using a cheap VPS and openVPN. You can also use it for other things such as running a very small seedbox or web seed, or a bittorrent tracker. The problem with this is that if you use legitimate details, the VPN could be traced back to you, but that's the same with VPNs that use a dedicated IP address who will cut you off, but using a shared IP address could mean a couple of software conflicts.
Do NOT use super cheap or free VPN because they datamine/keep logs.
You will likely be caught if you choose a VPN provider that keeps logs and are under constant pressure from anti-piracy organizations.
Seedboxes are basically machines on high speed connections that can download at super high speeds. Most of these "boxes" are dedicated servers that are already set up. They don't take much effort to setup and come with lots of space at an adorable price, also allowing you to setup OpenVPN if you want at the same price.
As a bonus, Seedboxes have the extra space, speed and isolation that you might need. Seedboxes make ratio-keeping much easier on private trackers and allow you to download at lightning fast speeds.
Using a Seedbox provider could, at it's discretion and jurisdiction, could release your details if you are traced back by them.
Exclusive private trackers often are faster, better and allow you to find torrents that aren't publicly available like little-known video games and movies.
You do however, have to keep a good ratio, and if you only leech... Good luck. In order to keep a good ratio, a seedbox or a fast and fat internet connection is generally required.
You also need an invite or you need to signup during open registration. r/trackers and r/opensignups are your friend as well as Google.
Some Private trackers sell your information, so use a fake persona whenever possible.
There is always the chance that a tracker is fake, or anti-piracy organizations have already infiltrated the website. Still take caution do your research.
If you are willing to pay for a file sharings service on high speed connections that will max out your connection, Usenet is a good choice. These servers are anonymous and are not actively being watched by anti-piracy organizations,
In short: I2P is a free, open-source, decentralized, anonymous darknet.
VPNs, seedboxes, private trackers and the like have one thing in common: the security they provide is mostly based on trust and obscurity. There are anonymization networks that do not rely on trust but rather on their technical architecture to provide anonymity to their users.
Your data is sent through multiple other computers running I2P (called I2P routers) before it reaches its final destination. Because the information is encrypted from end to end, no one will be able to see what you are sending, nor will they be able to tell what the source of the data or the destination is.
I2P already has a small but active torrent traffic. At the moment, you will not find the same amount of content as on the clearnet, but that of course will increase when the I2P torrent user base grows.
It should be noted that I2P is considerably slower than clearnet torrents. If you're all about speed, I2P probably isn't for you. But if you agree that trading off some amount of speed for a highly secure and anonymous way of filesharing is worth doing, then you should definitely give I2P a try!
Downloading using Open Wifi connections, hacked WEP connections and Coffee shops are somewhat, less orthodox ways of downloading without being caught. Though it's somewhat unethical.
Its possible to be caught if it is a honeypot dropper point, but it's extremely unlikely.
All else goes by the piracy 101 and basic internet reasoning. Again, do NOT use TOR, peerblock or Ultrasurf. These tools are meant for threatened journalists, anonymous free speech and whistleblowing, not so you can download the latest version of Photoshop.