Getting started with an Arduino Ethernet board (not shield)
The Arduino Ethernet requires either an USB-to-serial cable / board like the FTDI cables sold on various sites like SparkFun, Adafruit and eBay, or a low-cost external ISP like the TinyISP. 

Make sure you get an USB ISP with a 6-pin (3 x 2) connector, the (non-)standard that Arduino follows, rather than (or in addition to) the 5 x 2 pin ISP connector the rest of the world seems to favor. Alternatively, add a 10-pin to 6-pin ISP adapter to your order.

You cannot, in fact, even begin to communicate with the board directly over the ethernet port, without first setting its IP address and MAC address. (This last has nothing to do with the Apple Mac you may be using)

The FTDI cable connects to the 6 pin connector with the pins in a single row parallel to the board, while the USBTinyISP connects to the 6 pin connector right next to it, which has the double row of 3 pins each.