Hi, the original post asked what a new pilot could do to increase his piloting skills, and most of the replies seem to be related to checklist use.
There is another way to improve your skills, and that is to take several flights in a glider. You get to see climbs at 45 degrees on a winch launch, and descents at almost the same angle with full air-brakes and maybe a side-slip.
Also the adverse yaw is much more pronounced, with the real possibility of a good spin entry, if you step on the rudder at the 'right' time.
Thermal hunting is also a good practice for feeling how your machine is flying, and centering in a thermal is a whole new black art.
Gliding is a cheaper way of flying and is a whole new experience, which paid dividends in Mr Sulenberger's case.