In Hatchet, what is Brian's plan for landing the plane, and what conclusion can be drawn from his pre-crash actions?

Hatchet begins by introducing Brian as he boards a single-engine plane, piloted by a stranger, to go visit his father in Canada. During the flight, the pilot apparently suffers a heart attack and dies. Brian goes through various stages of panic and recovery, attempts to use the radio, and eventually resigns himself to the fact that the plane is going to run out of fuel and crash.

Brian mentally rehearses what he's going to do when the fuel runs out; the plane won't crash immediately, but will continue moving through the air. If he drops the nose, the plane will gain speed. If he raises the nose, it will slow. He determines that he needs to nose the plane down, gliding as gently as possible toward his target, and then nose up at the last moment, so the plane will stop quickly. He also determines that landing in a lake will be the best possible target, whereas landing in the trees will probably kill him.

Conclusions about Brian we can draw include;

• He is an adaptive person, and he can create and modify plans. This is evidenced by the change from his initial, frantic radio calls, to his calmer and more regulated calls later.
• He is emotional, but can control himself when necessary. He seems to understand, without stating it, that devolving into hysterics will not help his situation; nevertheless he is afraid
• He has had some exposure to, and a decent memory of, survival skills and basic rules of physics. For example, he remembers that he has to turn off the radio microphone in order to hear anyone.

How does Brian plan to land the plane when it runs out of fuel in Hatchet?

The sequence in question is in chapter 2.  The pilot of the plane has had a heart and has died.  Brian is in control of the aircraft and had been able to make brief radio contact with somebody.  After losing radio contact, Brian tries every ten minutes to raise somebody on the radio.  Throughout that time, Brian debates whether or not to take the plane down to the first clearing that he sees or stay in the air until the plane runs out of fuel.  Brian opts for the latter choice.  His plan is to put the plane into a shallow dive once the fuel runs out.  That will keep his airspeed up and air moving over the control surfaces.  That will give him some lift and rudder control.  While, in the shallow dive, Brian will direct the plane toward the nearest lake.  His plan is to crash the plane into a lake and soften the crash by pulling up at the last second.  That will trade air speed for increased lift, slow him a bit, and hopefully soften the crash landing.  

When the plane ran out of gas he should hold the nose down and head for the nearest lake and try to fly the plane kind of onto the water. That's how he thought of it. Kind of fly the plane onto the water. And just before it hit he should pull back on the wheel and slow the plane down to reduce the impact.

What is Brian's plan to land the plane in Hatchet?

Given the fear that is driving Brian at this point, there is no exact and specific plan that he formulates.  Brian is grasping at ideas to formulate some course of action because of being so overwhelmed by the situation.  One part of this "plan" is the idea to land the plane in a clear landing area of the forest.  Brian understands that the clear landing area is the only chance he has to make a bad situation a bit better.  Before this, his plan is to make contact with ground control so that they might be able to offer some help.  It comes to no avail, and when the plane's engine sputters, Brian realizes that he has to take that particular moment to negotiate landing the plane in a clear area of the forest.  As he tries to navigate his descent, Brian sees a  “a channel of fallen trees, a wide place leading to the lake.”  This is where his plan to land the plan ends up happening.  For Brian, this becomes an example of how his plans converge with some degree of luck that enable him to survive.  In seeing the open space to land the plane, Brian is able to negotiate the elements as best as he can in order to survive.