Buy Felling Wedges
Two plastic felling wedges will prevent your saw from getting pinched during a cut. You can find these at any outdoor power equipment store that carries chain saws.
Estimate the Felling Zone
Trees are taller than you think and reach farther on the ground than you'd expect. You can estimate where a tree will fall by using the “ax handle trick.” Hold an ax handle at arm's length, close one eye, and back away from or move toward the tree until the top of the ax is even with the treetop and the bottom is even with the base. Your feet should be about where the treetop will rest after falling. It's just an estimate, though, so allow extra room if there's something it might fall on!
Clear a Cutting Zone
Even when you're sure which way the tree is going to fall, you're still not ready to fell it. Cut away any brush around the trunk and clear two escape routes on the “non-falling” side of the tree. They should be about 45 degrees away from each other in opposite directions. The last thing you want is to trip while walking away from a falling tree.