Short answer
In the specific Project Setting, click the red "Delete" option, then confirm the deletion.
Full explanation
Go to the specific project you would like to delete
Click on the Settings button.
Click the red Delete (trash can) button at the bottom of the pop up list.
Read the confirmation, type "DELETE", and select Delete to finish.
Deleting a Project permanently removes its files and folders, Semantic Map, Email-to-Project settings, and chats tied to that Project. This cannot be undone.
Tips
Make a local copy of any files you may need before deleting.
You need the Manage Index permission to delete a Project.
Collections provided by AskTuring cannot be deleted by users.