I've tried to follow their instructions in Getting Started w/ Arduino on Mac OS X, but nothing seems to explain the specifics for uploading projects to the Arduino Ethernet. Do I need to configure a new bootloader? Do I need to get it connected to an Ethernet connection (not my computer directly)? Do I need to wire something up or get a serial-to-USB device of some sort? Do I need something like USB FTDI TTL-232 cable - TTL-232R 3.3V?
The link you provide to the product page explains what you need to do in the programming section.
Additionally, Adafruit, a Arduino partner/reseller says:
The Arduino Ethernet is literally just a Arduino Uno with a built in ethernet shield, and should be treated exactly the same. Well, minus the need for an extra usb-serial adaptor.
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.