Delete one contact
Open the contact.
Tap the menu in the header.
Tap Delete.
Confirm at Delete Card?
Delete several
On your contact list, long-press a contact, or tap Select.
Pick the ones you want, or tap Select all.
Tap Delete and confirm.
Deleting everything
There's no single "delete all" action. To clear your contacts, use Select → Select all → Delete.
If you're in a team
Deleting a contact you own and have shared removes it for everyone.
FAQ
Can I get a deleted contact back?
No. There's no trash or undo.
Does deleting a contact remove it from my phone's address book?
No. If you used Save to phone, that copy is your phone's, and stays.
Does deleting a group delete its contacts?
No. The contacts remain; only the group goes. See Organizing your contacts.