Download the Arduino Environment from: http://arduino.cc/en/main/software and extract the files.
Unpack your TinyDuino - you should have something that looks like this:
Connect the TinyDuino Processor Board to the TinyDuino USB Shield.
Connect the TinyDuino to your computer via a micro-USB cable.
Install the drivers for the FTDI chip: http://www.ftdichip.com/Drivers/VCP.htm
Launch the Arduino Environment and navigate to Tools > Board and select the Arduino Pro or Pro Mini (3.3V, 8MHz).
Remember, the TinyDuino is 8MHz, not 16MHz!
If you like, you can run a test program by navigating to File > Examples > 01. Basics > Blink
Select your serial port by navigating to Tools > Serial Port (on Windows, most likely COM3 or higher – on MAC, something like tty.usbserial-XXX…)
You're all set up to upload the program - you will see the RX and TX lights flash when you do. Assuming you programmed the Blink program, you will now see the green LED flash on the Processor board.