How to use driver?

I also do not use arduino but I converted these sources for other MPUs.
See app note here [url]http://wiznethome.cafe24.com/wp-content/uploads/wiznethome/Chip/W5100/Application%20Note/W5100_Application_Note.zip[/url] for DHCP and DNS examples calls routines that interest you instead In what you have already downloaded there are routines ( in modules W5100.c and socket.c) for W5100 registers and listen function.
For the server mode setting sequence instead look here [url]TCP Example] is for the W5500 but is practically the same.