I haven't hooked up this particular model of Sony, but have hooked up another DVD player with a standard ethernet port that the Sony appears to use.
To do this using Apple components, you will need to have an AirPort Express(n) located near the player. The Express should be configured to "join a wireless network" and "enable ethernet clients" needs to be checked on the Wireless setup page. Of course, the Express will need a strong enough wireless signal at its location to be able to connect. The Sony manual mentions a Linksys device to accomplish the same task. Your post did not indicate what device you were trying to use at the DVD end.
If wireless will not work, take a look at a pair of ethernet powerline adapters to accomplish the same task as if you were directly connecting your router and the Sony using an ethernet cable. Ethernet is by far the best way to connect devices if you are planning to stream video signals. Wireless may or may not be able to handle the required bandwidth for video.
Most Audio/Video devices will auto-connect to a network just as your computer does, but it is important to restart the DVD player once you have the connection made before you click "connect" on the devices on screen setup menu.
