What did Brian do after the plane engine died?

In chapter 1, Brian boards a plane to go to Canada to visit his father. His parents had recently gotten divorced:

So this summer, this first summer when he was allowed to have "visitation rights" with his father, with the divorce only one month old, Brian was heading north.

Brian's dad is a mechanical engineer working in the oil fields in Canada. Brian is going to Canada from New York with "some drilling equipment" for his dad. He flies in a bush plane with only the pilot and himself on board. While traveling, the pilot has a heart attack. Thankfully, he had shown Brian how to fly the plane before his heart attack:

"Good plane like this almost flies itself. . . . Makes my job easy." He took Brian's left arm. "Here, put your hands on the controls, your feet on the rudder pedals, and I'll show you what I mean." . . . Brian reached out and took the wheel in a grip so tight his knuckles were white. He pushed his feet down on the pedals. The plane slewed suddenly to the right.

The pilot's training allows Brian to steer the plane after the pilot's death:

He had to fly it somehow. Had to fly the plane. He had to help himself. The pilot was gone, beyond anything he could do. He had to try and fly the plane.

He tries to communicate with someone using the plane's radio; he gets through to someone and has a short broken conversation that is not helpful:

It all seemed so hopeless. Even if he did get somebody, what could anybody do? Tell him to be careful? All so hopeless.

He soon realizes that the plane will eventually run out of gas; he either has to "wait for the plane to run out of gas and fall or he could push the throttle in and make it happen sooner."
He decides to continue flying, but he thinks of a plan while the plane moves:

When he ran out of fuel the plane would start down. He guessed that without the propeller pulling he would have to push the nose down to keep the plane flying . . . He would have to push the nose down to keep flying speed and then, just before he hit, he would have to pull the nose back up to slow the plane as much as possible.

Brian decides to let the plane run out of fuel, but he thinks about how he will bring the plane down without crashing to the ground. He decides, also, that he will need to find a clearing to land in. However, there are no clearings in the woods. Instead, he decides he will need to land in water.
When he finally runs out of gas, he pushes the nose of the plane down, as he has planned. He scans the ground to find a lake; then, he steers the plane towards this lake. Despite his great fear, he manages to land the plane in the lake:

Then a wild crashing sound, ripping of metal, and the plane rolled to the right and blew through the trees, out over the water and down, down to slam into the lake, skip once on water as hard as concrete, water that tore the windshield out and shattered the side windows, water that drove him back into the seat.

Brian then fights to get his seatbelt off and escape through the broken front window. He makes his way out of the water and to the shore. Now, he has to figure out how to survive alone in the woods.