EvilZone

KISS; Keep it simple stupid. It's better not to have too complex set up, that means more points where your anonymity can fail and betray you. This is a hard question to answer, it's so general.

Ask yourself this instead: What's my threat model? Who is my advesary and who am I up against? A nationwide state? An repessive regime or just a script kiddie trying to dox you? It depends on the situation you're in, they require different levels of OPSEC. Chances are that you shouldn't even be using internet if you're trying to evade a nationwide state trying to track you down, they have many resources available.

First and all, this applies to everyone who wants to be anonymous. Shut the hell up, silence is security. Don't talk about your plans, futhermore check out this talk which explains more: OPSEC for Hackers https://www.youtube.com/watch?v=9XaYdCdwiWU

There's many approaches for the so called paranoid set ups. But as a first step I recommend you to use Tor. Despite what people say about Tor, it's still better than a vpn. Because a vpn is only one hop away, and they won't go to jail for you. Some things that you should have clear when using tor, don't run scripts, don't contaminate your circuit with your clearnet activies and use SSL when possible. If you want to patch things up even more you can use a vpn. Using a vpn before tor will give you more security by encrypting your communications (guard node and exit node can see your traffic unencrypted iirc). Or you can do it the other way, a vpn at the end of the circuit which gives you more anonymity instead.

Some of my favourite approaches for using tor:

1) Virtual Isolation
Isolation is good practise. By isolating your Tor traffic on a virtual machine, you can 1) route all of your traffic through tor 2) even malware with root access wont find out your real IP address. You should be using whonix for this: https://whonix.org

Topography:
Computer > Virtual Machine [ Tor gateway > Whonix Workstation] > Internet
Note: Yes, you can use a vpn outside the VM to make it more secure.

2) Physical Isolation
This is the same thing as above except you're using physical machines for the Isolation. This can be done through PORTAL (Personal Onion Router To Assure Liberty) with the help of a raspberry pi or an openwrt router.
 
3) Tails LiveCD
I really like this, because it leaves no trace and pretty much runs in ram. Just keep it on a usb, DVD ROM (Read Only makes it harder to tamper with), SD card (Easy to dispose of) etc. And boot it up on the computer, it's also pretty useful in public places considering you can use a window xp theme to make it look fairly normal.

That is really just one small piece that can get you started with this. There's tons of interesting ways to enchance your anonymity.