This is a very practical guide to stay anonymous. Online privacy is not about having something to hide, it is about having everything to protect. Trackers and advertisers see what you do online. Everyday. Every second. This could become public one day, that's why you should care about privacy. Keep in mind that the techniques I describe here are open to everyone. If you are a new Edward Snowden, you will need more complex tools. But if you want to protect yourself in a reasonable way, what follows will work for you.
Craft a new identity
Do not use your personal email address. Do not use your work email address. Instead, craft a new identity. If you are not inspired in finding good names, just browse to Fake Name Generator. Fake Name Generator will create a new identity for you.
You have just crafted your new identity. Now it is time to create a new email address. Do not use Gmail. Go to Tutanota or Protonmail and create one without using your real name. If you really care, use Tor to browse to the mail provider you have chosen. Tor is free software for enabling anonymous communication. Tor directs Internet traffic through a free, worldwide, volunteer overlay network consisting of more than seven thousand relays to conceal a user's location and usage from anyone conducting network surveillance. Just download Tor browser to browse anonymously in seconds.
Remember to create a long random generated password and store in a proper way. I do not like cloud services that manage my passwords. I can't trust them. Instead, use KeePassX (for Mac users) or KeePass (for Linux or Windows users). You are the only one who owns the password file. If you need to store the password file in a zero knowledge cloud I suggest Spideroak. That's my choice.
Receive an SMS
Many services ask you a telephone number to verify your identity. If you need to receive SMS, Receive-sms.com is a good solution I use. Another one is receive-a-sms.com. There a lot of good services and they are very similar, so feel free to choose the one you like more.
If you need pay you have two alternatives: bitcoins is a good solution. Otherwise you can pay using a virtual card such as Entropay.
A VPN basically takes your Internet connection and makes it more secure, giving you a temporary IP address while hiding your true IP address. If you need a good VPN, I trust the bright guys at F-Secure. F-Secure's freedome is my VPN to go.
Your confidential cloud
If you need a confidential cloud where you need to place sensitive data, do not use Google Drive or Dropbox. But SpiderOak. SpiderOak is the only zero knowledge cloud I trust.
The perfect distro
If you love Linux as I do. Just download Tails. Tails is a live Linux distro you can start on almost any computer from a DVD, USB stick, or SD card. It has everything you need and helps you in leaving no trace on the computer you are using unless you ask it explicitly. You are much safer if you are using Tails instead of your OS of choice when you are online.
Last but not least, if you care about privacy, donate to the Electronic Frontier Foundation. They are amazing people who do a great job building great tools and helping privacy.
Have a great day and stay anonymous,