A King account allows you to play with other active players, save your progress so you can keep playing on other devices, and more! You can learn more about all the benefits of a King account in this article: What is a King account?
To create a King account:
Open the game and tap on Retrieve My Progress/ Played before/Save my Progress (depending on the King game)
Select Sign up with email (green button)
Fill in with your email address, password, first name (which will be publicly displayed)
Don't forget to save your email and password so you can access your King account in the future.
You're all set! Now that you have your own King account, it's time to make full use of it and go play!