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.
Step 4: Now What?
I have no depth perception. That's why they wouldn't let me fly jets.
It fell in the right direction, but it skinned the next tree over and hung up in it.
There are always problems like this. This one's called a "widowmaker" because you've just compressed the spring of a giant trap, and now you've got to walk into it and saw through the trigger.
A digression: In the lower left of this frame you see a couple of handsaws laying on the ground. Those are old "bow saws" also called "swede saws" because of where they were invented.
One of our old Minnesota neighbors cut firewood for a living with a big old crosscut (cuts on both strokes) two-handed handsaw in the thirties. He was just getting by selling four cords (a unit of measure for firewood) a day. Then he bought one of the new Swede saws, started cutting 8 cords a day, and had enough money to get married.
The tubular steel bow puts the blade under high tension so the blade can be very thin without puckering, and because the blade is narrow it won't bind in the kerf as much. So they can cut a very narrow kerf, removing less wood, and do it fast with less work than previous saws, which weren't much different from what the Romans had.
Step 5: Saw Up From the Bottom
Saw up from the bottom until the tree starts to sag, using the upper edge of the saw.
In the photo you can see the sawdust being shot forward.
This is a dangerous cut.
If the saw binds up it can kick back and alter your appearance.
Then saw down from the top until a good outcome ensues.
If it looks like the saw might bind in the top you can cut a notch instead of a single cut.
Step 6: Check Yourself Into the Clinic
I stand in awe at the sight of this forest giant laid low.
If things don't go so well, your loved ones will get to contemplate your own mortality.
I think I'm done playing with chainsaws for the day. That log will make a great bench just the way it is.