Hi Panda,
Trusting in the higher power could simply mean releasing your sense of control over every aspect of your life. Adjusting your outlook to accept that the world, the universe will continue to follow it's own laws and you're just along for the ride so to speak. And in the end, if you roll with the punches, if you're flexible, you'll be able to adapt and survive. That all in all, at the end of the day, it'll all be alright
Cuz nothing will happen that wasn't supposed to happen.
I think that is essentially what turning yourself over to your higher power means.
hope that helps.