This turning on by itself should not happen, and usually means that something is messed up. When it happened to me, I was still able to get it into DFU mode:
1) Turn off the device while plugged in.
2) As soon as it is off (or immediately after it starts coming on) press Power and Home. You actually have around a second after the apple logo appears to do this.
3) Keep pressing Home and Power for ten seconds. The Apple logo will disappear after around 8 sec. Sometimes the screen will briefly flash the "connect to iTunes" screen before turning off, that is OK as long as it turns off.
4) Let go of the power button, but keep holding the Home button for another 10-15 sec.