How to recognize the hand of God?

In Luke 4: 1-13 the devil subjects Jesus to a series of tests. In one of them he challenges Jesus to jump off a tall temple, taunting him, that if he is truly the son of God, surely God will save him.  

12 Jesus answered, "It says: 'Do not put the Lord your God to the test.'

This story made a great impression on me as a child, and it's something I still ponder about. How does this story translate to day to day life, and how do I live by it? For example: I can certainly understand I should be careful crossing the street, and not just trust God to rescue me from a nasty demise by a big lorry!

On the other hand, I read and hear a lot about letting things go, and putting one's trust in God's hands. To trust things will work out just the way they were supposed to.

But how do you know when to trustingly let go and when to take action? When is it time to do something and when is it time to simply say: 'Thy will, not mine be done'?

And how do you recognize the hand of God? I certainly wouldn't want to be this guy!

A man is caught in a flood. As the waters rise, a boat comes along and offers the man a ride to safety.
“No thanks,” the man says, proud of his level of faith in God, “I believe God will save me.”
“Suit yourself,” the man in the boat shrugs, as he drives off to help other people, and the waters continue to rise, forcing the man to the second floor of his home. However, as we waits for the hand of God to personally save him, another boat comes along and tells him to get in while he can, because the flood waters are showing no signs of receding.
“No thanks,” the man again says proudly, emboldened by the unique opportunity to prove his faith in God. “I believe God will save me.”
“Suit yourself,” the man in the second boat says, shaking his head, as he veers off to help other stranded homeowners. In the meantime, the rising flood waters force the man to his roof, where he is finally spotted by a rescue helicopter.
“Grab the rope and climb aboard,” the man in the helicopter yells to him above the din of the rotating blades.
“No thanks!” the man on the roof yells back, still certain that a miracle will happen to save him from drowning. Therefore, unable to convince the man to climb into the helicopter, the rescue team goes off in search of others willing to be rescued.
Sure enough, the water rises to the roof, and then above the man’s head, and he drowns. Shortly after, he finds himself in Heaven, waiting to be brought before the Heavenly Court. After some time, and a lot of angry pacing back-and-forth by the drowned man, an angel comes out to call him in to the inner chamber. However, before the Chief Magistrate can say a word, the man bursts out and cries,
“Where were you?! I invested all of my faith in you, that you would save my life as you always promised you would if I had faith, and you go ahead and let me drown! What kind of reward for faith was that?”
For a long moment, there is silence in the Court Room, as if the man has made a valid point. Until, that is, the Chief Magistrate leans forward and says calmly, but firmly,
“What do you mean? Who do you think sent you the two boats and the helicopter?!”

I have so many questions.
Should I take action to find the answers, or should I wait for them?