To delete site:
Click on My Site
This takes you to a page with a list of options (My Home, Statistics, Plan etc.) The penultimate option is Manage.
If you click on this it has a menu (Domains, People, Settings).
Click on Settings, it takes you to the settings of your site.
Scroll down to the end of the page, it gives you an option to Delete your site permanently.
Click on this, it tells you what will be unavailable (i.e. everything)
Click on Delete Site, it asks you to fill out the website address and then you can delete it.
There’s an article guiding you through these steps here https://en.support.wordpress.com/delete-site/
After that, to create new site:
If you already had more than one site, scroll down the left hand side menu on My Site and click ‘Add new site’.
If the one you want to delete is your only website, then if you click on My Site it will give you the option to make a new site.