Thankfully this bit was way easier than I thought - the team behind the Arduino library have done a pretty awesome job. I'm not going to duplicate the steps here - the Github page does a great job of explaining it.

Now you should be able to pick the "Generic ESP8266 Module" from the board list. I had to make a guess at the settings, as I had no idea what type I had - the defaults were fine in my case.

Don't forget to select the right port after you have plugged in the FTDI cable (Tools > Port) - on my Ubuntu machine it switches between /dev/ttyUSB0 and /dev/ttyUSB1 every time I plugged it in, so if you can't upload code - check that the port hasn't changed.