Theming views and overwriting the default file upload display
You don't need to use a template or get your hands dirty with code.

Just add the field to the view twice.  Hide the first field from display, but change the formatter to "URL to file".  Rewrite the output of the second field to "Download PDF".  On the second field, select output field as link and assuming your field is named 'pdf', make the path [field_pdf].