In general, contacts can be deleted as usual from the device contact list.
If you have tried to remove the contact from your device, and it can’t be removed, then the contact may be synced from another source such as Facebook or Gmail.
In order to remove contacts that come from other sources, you will need to go directly to the source and disable syncing/linking with that account to the device.
On iOS linking with other sources especially can cause duplicates. More info about this may be found here:
http://syncme.helpshift.com/a/sync-me-contact-sync/?s=troubleshoot&f=help-i-have-duplicate-or-multiple-contacts-iphone