Hi there. Open Contacts, click on the contact you want to delete, click on "Edit" button (bottom left of contact), scroll to the bottom of the contact and click on red "Delete Contact" button - contact's gone. Hope that works for you.
Groups can only be managed via iCloud or the Mail app on an OSX device. Nor will deleting a group delete the contacts in it. This will not help you on an iPad unless youa re syncing contacts through iCloud.