What is the proper way to use a hand plane on wood?
The concept of a plane:  It uses a very sharp chisel like blade mounted in a body to remove a thin layer of wood.  In practice, you use both hands (for control and even pressure) to slid the plane in the direction of the wood grain to remove a thin layer of wood at a time.  

For effective use, you will need the piece of wood you are planing to be firmly held in place.  Use clamps, not someones hands, to hold the wood.  The blade on the plane needs to be razor sharp (reason for not using hands) to effectively grab the wood and shave it.  If it is dull, it is just going to skip and mar the wood.  You will need to find the right amount of pressure you will need to pressure to keep the blade in the wood.  Also don't try planing off too much at once.  The deeper you set the blade, the more likely it will mar the wood.  Start razor thin at first and gradually cut more as you get used to it.

For best results, do full strokes along the wood.  Where you start and stop it is easy to create mars in the wood.  Also if you do short strokes it is easy to create an uneven cut.  A good way to see if you are cutting evenly into the wood is to create a scribe line where you want to plane the piece to.  

As @Keshlam said in the comment, use some scrap first.