First step - find a tree to cut down. No problem. As soon as you know how to cut down a tree people will sense it and constantly ask you to cut down trees for them.
It will help if you know some of the technical vocabulary:
Equipment: Every piece of equipment used in this process is called a "Widowmaker".
Tree Anatomy: The tree and every part of the tree is called a "Widowmaker".
Terrain Analysis: Everything in the vicinity of the tree is called a "Widowmaker".
Act really confident and relaxed as shown in this photo. (pics by ex_mo)
I'm saying "you mean this tree over here?"
Step 1: Cut a Notch in the Felling Direction
The "mouth" part of this notch faces in the direction you want your tree to fall.
If the tree is mostly upright and the branches are sort of symmetrical it will want to fall that direction.
We tied a rope to the top of the tree to help it fall in the direction we wanted.
Step 2: Cut Toward the Notch from the Other Side.
When you get close to the notch the tree will start to lean away from you. If it doesn't, or if it leans the wrong way and binds your saw blade, have the Oompaloompas pull on the rope tied to the top of the tree.
Step 3: The Tree Falls
There isn't any very safe place to be, because branches can break and fly anywhere, or the top of the tree could pull something down with it.
If you didn't cut all the way to the notch you can leave a sort of "living hinge" that will keep the tree from falling to the side.
My cousin's father-in-law was killed by a vine that got pulled by a tree as it fell.