Programming an ATMEGA2560 using FTDI
If you have a bootloader, you just need to connect up four wires from the FTDI cable:


Pin 1 (black) -> Ground
Pin 2 (CTS)   -> not connected
Pin 3 (Vcc)   -> 5V
Pin 4 (TxD)   -> Rx (Mega pin D0)
Pin 5 (RxD) -> Tx (Mega pin D1)
Pin 6 (green) -> not connected




This will not auto-reset, so you will have to press (and release) the Reset button on the board at the moment that the sketch starts to upload.




  How to make it auto reset?


What you should be able to do is connect RTS to Reset on the board, using a 0.1 µF capacitor (in series). I found in practice that this did not bring Reset low enough to trigger it - I'm not sure why, except maybe the board has a stronger pull-up resistor on /RESET than expected. That technique works for me on breadboard Arduinos.

Since it didn't work for me, I did not put it in my original answer. You could try that, and if it works, well and good.