How do customize the HTML output around a specific field using field.tpl
You need identify the field machine name. For example if you have a field called Name and have a machine name field_name the field tpl name should be field--field-name.tpl.php. 

See this thread as well as it provides a comprehensive guide on how to override field template using hook_theme and preprocess function. 

One of the most handy helper I used is $conf['theme_debug'] = TRUE; in settings.php. It will show a template suggestion in HTML source.