Depends on the device/Contacts app you're using, but usually long-pressing a contact will not allow you to edit it (most of the time just delete and/or share). To edit a contact's details on most apps you have to be seeing the contacts details (sometimes tapping a contact name will take you there, some other phones require an extra step and select DETAILS). Once in that view (where you can see the name, phone numbers, addresses, etc.), you should either see the EDIT option there or a menu button that contains said option.