So first things first, there is no such thing as COMPLETE ANONIMITY.
You can however protect better your identity and your data from theft or misuse by simply understanding the dangers related to the activity you want to realize.
Example: If you would conduct any illegal activities on the same computer that you would use facebook or gmail or anything that could be related tou you, you probably would get caught very easily.
However if there was nothing that could trace the source of your activity back to you it would be much harder to be tracked down.
So you can probably tell by now that no matter how secure your system/network is it wont protect you against your own errors.
And always remember that the resources used on security should always be more or less equal to the value of the data stored
So what will you need to start ?
1 - Well you do need a computer but if you're here i guess you already have one.....
If you personally bought the computer or the parts you can be tracked by their serials, or for wireless devices mac adresses but those can be spoofed easily.
2- Choosing the best OS
Honestly in my opinion there is no such thing as "The Most secure OS" there are however linux distribuitions that focuse on security like Debian or Red Hat and some OS's like Qubes and Tails wich are also linux. I really dont recomend windows because it stores and collects more data than needed. I've read somewhere that you could modify windows by deactivating some services and stuff and it would be better but i really wouldn't go for all that trouble.
3- Encryption
You should always encrypt your hard drive to prevent phisical access and you should protect your bios with password and the same goes for Grub so that there is no chance of modifying your computer's startup. ( you can even disable the usb ports or ethernet its up to you)
So that was for physical access now comes the hard part wich resides in online access.
Never input highly sensible data in websites especially the ones you dont fully trust, even if it has https because nowadays if you are a target of a Mitm attack, https could be easily downgraded and your data captured or you could be redirected to a fake page that looks like facebook's login page or any other website, and you would directly send your info to the attacker
The same applies to public wi-fi you should never log into your accounts on public wi-fi.
4- For the browser part DONT USE CHROME
Google tracks a lot of your data so just dont .....
Use firefox or opera or iceweasel... wich i dont recomend (since its firefox for linux but slightly modified so they wouldn't have legal issues )
Check that your browser doesn't store any offline data especcially passwords since it doesn't encrypt them (you could use a password manager but those too are susceptible to attacks).
Modify your browser configuration and disable everything that might compromise your true identity ( Just search "firefox about:config security").
Also search "My browser info" and check what info your browser outputs.
For search engines dont use google.
Just dont...
Use DuckDuckgo or something else......
5- E-mails
I dont think it is necessary to say anything more about google so g-mail is out
You could use proton mail however it doesnt work for me so cant help you much on this one you could however build a mail server but there are costs involved.
There are many others but with a quick search you will find the most known ones.
6- IP address
I'm not going to thread deep on this topic because there are a lot of ways you can spoof or hide your Ip adress, but here are the main ones.
- TOR - Tor is what you probably think of when IP spoofing is mentioned but as many know tor has its vulnerabilities and it does not protect you from the errors you make, even if you use bridges to hide the fact you are using tor you can still be tracked.
- VPN - vpn or Virtual Private Network routes the traffic from your computer trough their servers to your desired website, some are free some cost money, but you are still passing your information trough the hands of someone else's computer.
- WHONIX - Whonix acts like your own vpn but relies on virtualbox or Qubes and it routes one or all of the workstations traffic trough it and then trough tor so it appears that its coming from a diferrent machine
- PROXYS - I dont recommend proxies you could add a proxy to some of the other options above but remember more loops equals more time to reach destination
- PUBLIC WI-FI - Public wi-fi can be a danger but can really make you almost invisible when all of the other precautions were made and if you were tracked down it would be to some random shop or mall etc...
Now i made this guide so that everyone that read it would better understand the risks in online activities.
I am not responsible for the misuse of this information for other objectives that might end you up in trouble.