The first question is not how to stay anonymous, but how you can be tracked.
Even if you tunnel tor in a vpn and use proxy chains, there are information that can reveal you. You are just hiding where you come from, not who/what your computer sw/hw are.
HTTP. That can definietly pwn your anonimity. Your browser / programs /etc has signitures that can be tracked back. Let's say someone thinks user agent in a browser 'haha pwn yo don't know my usheragent' is a good choice because it hides your real agent. Not really. It may hide what is your default agent, but that information will be logged on the servers you are visiting with many other settings that can be fished. It's not so hard for higher level agencies to find to servers where a stupid user agent appears (eg FinFisher which provide penetration for government -
http://www.finfisher.com)
So how to set up a safe browser?
Check
ip-check.info to see what can be read from your browser and fix the issues.
Check
panopticlick.eff.org to see how unique your bro is.
Lear more. Use add-ons if needed. These are just basic sites.
Summing the question:
What do you send through a network? How can that be tracked back? What routes/encryption/NAT to use?
After this I would like to get some ideas from your side too. What do you use to keep your information safe. Don't post something like "use vpn".. we all know that and alone it's really not a big protection. Detailed posts please.