Open the Contacts app or Phone app
Tap the contact you want to delete
Tap Edit
Scroll down and tap Delete Contact
Repeat for each contact you want to remove
To delete multiple contacts at once, use iCloud on a computer
Sign in to iCloud.com
Open Contacts
Select multiple contacts using Command-click on Mac or Ctrl-click on Windows
Press Delete
Confirm the deletion
Make sure Contacts syncing is enabled on your iPhone
Wait for the changes to sync to your iPhone
To remove all contacts, turn off Contacts sync in iCloud settings and choose Delete from My iPhone when prompted