The delete button is right there where the help page says it is.
To shut down a project using the Cloud Platform Console:
Open the Settings page in the Google Cloud Platform Console.
Click Select a project.
- Select a project you wish to delete, and click Open.
- Click Shut down.
- Enter the Project ID and click Shut down.
Please note that there is a 7-day grace period before the project is actually purged from the system. Which means you won't be able to immediately create another project with the same name.
As of July 2017 you can set budgets that send notifications via email but do not cap spending:

To set an alert-only budget, which will not cap spending:
Official help page: https://support.google.com/cloud/answer/6293540?hl=en