I think you’re looking at the situation wrong. You are thinking “How do you wake up on time?”, when the real issue is “Why should there be a time you have to wake ?”
I don’t know where I got this from – I’m not a Buddhist. I did take an interest in the religion at one point in my life though, and I recall stumbling upon a quote from a monk (the Dalai Lama?) about daily routine. The suggestion was that a Buddhist should arise quickly in the morning and strive not to be regretful for leaving the coziness of sleep, and a Buddhist should meditate first thing, to prepare the mind for the coming day.