Please log in, go to "Account settings" and then follow the "Delete Doodle account" link.
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 can't log in as you forgot your password, please read here how to reset your password.
If you logged in with a Google or Facebook account you need to reset your password as well. Read here.
It won't change your Google/Facebook account/login, just creates a new Doodle password. Use this new password to delete your account.
Please be aware that deleting a Doodle account will not delete your Premium Doodle subscription, if you have subscribed to one. Please reach out to Support if you have a running subscription and plan on deleting the account.