Admittedly this is a partly rehash of what exeng has just said, but regardless of what USB-to-serial you use... the two mains tricks are to cross over the TX and RX, and to GND P2 so the Oak goes into Serial Upload mode. So GND goes to GND, RX of the USB-to-Serial goes to P4 (TX) of the Oak, and TX of the USB-to-Serial goes to P3 (RX) of the Oak. And P2 goes to GND also. You then power up the Oak via microusb connector or some power supply. and then you run the update script.
To test at your adapter to some extent, you can simply connect TX of the adapter to RX (female to female lead, a jumper, paperclip, whatever), fire up the Arduino IDE and open the serial monitor (or some other suitable serial terminal program)... making sure you choose the right COM port under Tools -> Port before doing so, and try sending some text. If it echoes back, both transmit and receive on the USB-to-Serial are working. You can confirm this by removing the loopback (jumper/wire), and when you transmit (type and press send/press enter) it shouldn't echo back.
