You can ensure your own safety by following a few precautions. Be certain your ladder rests on a firm base; if the ground is soft, set the ladder on some planks. Lash taller ladders to the tree and have someone hold the base of the ladder while you work. But keep other spectators away. And note where the limb will fall, making sure its drop won’t injure people or plants. If its fall might damage a valued shrub, say, tie a rope around it, pass the rope over another limb higher in the tree, and lower the cut limb slowly to the ground.
There are many reasons why you may need to remove a sizable limb from one of your trees. The limb may be damaged, diseased, or dead. It may be rubbing against another branch. Or it may just displease you; the tree would look better, you decide, without that particular branch. Any limb with a diameter greater than one inch should be sawed. For limbs up to two inches in diameter or even slightly larger, and for limbs growing close to another, a narrow, curved pruning saw is the ideal tool and is easy to use, as it cuts by a pulling rather than a pushing action. For cutting larger limbs, a straight pruning saw with teeth on both sides of the blade can be used. But handier for most amateurs (because it can be used for jobs other than pruning) is a bow saw, which has a detachable blade mounted on a C-shaped frame. In any case, do not use a chain saw, which is far too perilous for someone balancing on a ladder.
Now, another way to trim your trees, is with a pruning system. You eliminate the use of ladders, which makes it a lot safer. Fred Marvin pruners are used by professionals, everywhere, but they are also available to homeowners. They are lightweight, and easy to use. They are made of high-grade steel to permit several resharpenings, for a lasting and durable pruner. You can use use longer poles, to reach higher limbs. You can use special pruner heads, for trickier pruning.