Log into your account and go to to your account settings. Scroll down the page and click on "Delete Doodle account".
You will then be asked to fill in your password for confirmation. Once you fill it in and click the button 'Yes, delete' your account is deleted.
In case you cannot log in because you forgot your password, please read here how to reset your password.
If you signed up for Doodle with a Google, Facebook or Microsoft account you need to reset your password as well. Read here. It will not change your Google/Facebook/Microsoft account/login - It just creates a new Doodle password. Use this new password to delete your account.
Please be aware that deleting a Doodle account will ALSO DELETE YOUR PREMIUM SUBSCRIPTION if you are currently subscribed to one. It will cancel any scheduled renewals. A refund will not be issued.