Open the Contacts app or Phone app
Tap the contact you want to delete
Tap Edit
Scroll down and tap Delete Contact
Tap Delete Contact again to confirm
Repeat for each contact
To remove all iCloud contacts at once
Go to Settings
Tap your name
Tap iCloud
Turn off Contacts
Choose Delete from My iPhone if prompted
To delete all contacts from iCloud
Go to iCloud.com
Sign in with your Apple ID
Open Contacts
Select all contacts
Delete them
To remove contacts synced from another account
Go to Settings
Tap Contacts
Tap Accounts
Open the account
Turn off Contacts or delete the account
To erase everything on the iPhone
Go to Settings
Tap General
Tap Transfer or Reset iPhone
Tap Erase All Content and Settings