Open the Contacts app on your iPhone
Tap the contact you want to delete
Tap Edit
Scroll down and tap Delete Contact
Confirm by tapping Delete Contact again
To delete multiple contacts, open Settings
Tap Contacts
Tap Accounts
Select the account that contains the contacts
Turn off Contacts for that account to hide them (or delete the account if you no longer want it)
To delete contacts from iCloud: go to Settings > [your name] > iCloud > iCloud Backup (optional)
Go to Settings > [your name] > iCloud > Manage Storage
Tap Contacts (if listed) and delete as available
To delete contacts from Gmail/other accounts: go to Settings > Contacts > Accounts > [account] > toggle Contacts off or remove the account
To delete contacts in bulk: use iCloud.com on a computer, sign in, open Contacts, select contacts, and delete