There's more than one way to do it, but here are the steps I would take if I was new at this...
(1) Buy an Arduino... I'd get either the RBBB or the BBB from
Welcome | Modern Device. RBBB and BBB are two different versions of the Arduino; either will work well. ModernDevice is a great company. You can get pre-built versions of their versions of the Arduino if you're not comfortable soldering all the bits on the board, or are in a hurry, or lazy, or whatever.
(2) Now you need a cable to connect the Arduino to your computer in order to put the code into the Arduino. If you're ordering from ModernDevices, you can get their USB-BUB board...
USB BUB Board | Modern Device You can use any FTDI cable though, and maybe you have one, or can find one cheap somewhere else. FTDI cables plug into your computer's USB port, and basically turn it into a serial port. FTDI is supported by Linux, OSX, BSD, windows.
(3) Now go to
Arduino - HomePage and download the Arduino IDE. Maybe read some of the "Getting Started" section...
Arduino - MacOSX
Arduino - Windows
... that link gives very clear instructions on how to, well, get started, including connecting the Arduino and uploading code to it. They show you how to test the arduino by making an LED blink. I do this with every Arduino I build. The steps are very easy to follow, and there's a large community of people (IRC and Forums) willing to help, and be nice about it.
(4) Once you've got the LED blinking, you should have no trouble ULing the code for the servo controller, but if you need specific help, come back here. Of course, you have to build the circuit too.
Hope that gets you started.
PS, my semester just ended today, and on my summer to-do list is more servor/motor control projects. Here's hoping I get around to it.
Nathan