If you're looking for a way to remove a dead tree and avoid calling an experienced tree removal service there are several things to seriously consider. Tree work, although it looks easy, is full of many uncontrollable and unpredictable forces.
If the tree to be removed is near a powerline, a house, a fence, a septic tank, or any other item of importance, it is generally a good investment to simply call on a tree company. If the diameter of the tree is less than about 6 inches or so, keep reading.
At 6 inches or less with little brush to handle, to be sure the tree falls where you want it to fall, attach a rigging rope ($50-$100) to a point on the tree towards the middle to top whereby you can have someone pull on the tree (someone strong and agile) to coax it in the right direction. Once secured, making sure that everyone is paying attention and clear of the fall zone (or ready to quickly clear the fall zone), make your notch cut on the side of the tree in the direction you want the tree to fall. In other words, if you want the tree to fall to your left if you're looking at the tree, make a "V" shaped notch in the tree on the left side.
Once your notch has been cut, proceed to cut the other side of the tree to be removed inwards towards the "V", making a "hinge" whereby the cut is slightly above the "V". This hinge will help prevent the tree from sliding backwards and help you direct the fall. With the helper pulling the rope attached, give warning when you feel that it is going to drop and yell "timber!".
It is quite an exhilarating moment when the tree falls to the ground!
If the tree is larger than 6" or so in diameter or if you simply want to leave it to a company who has experienced climbers and linemen, call on a tree removal company. Experience in climbing, saws, ropes and knots, and those unpredictable moments definately count, in my opinion, where tree work is concerned.