There are 4 things that determine your final drive ratio: crank length, chainring size, cog size and wheel diameter. Crank length and wheel diameter don't change while you ride. However, when you change gears in the front, the crank-to-chainring ratio changes, as does the chainring-to-cog ratio. When you change gears in the rear, then your chainring-to-cog ratio changes, along with the cog-to-wheel ratio.
In terms of turning the cranks, using a larger chainring actually gives you LESS leverage--the resistance (the chain) is farther from the fulcrum (the center of the chainring) and closer to the applied force (which is at the pedal axles). The net effect is that, with a larger chainring, it takes fewer turns of the crank to cover a certain distance, but requires more input force from your legs. On a steep enough incline, you may not have the necessary leg strength to even move the bike, much less do so efficiently and without injury.