If you have only one or two trees, you may only need a pair of hand shears and a small, lightweight pruning saw.
Hand shears will cut branches up to ½ inch in diameter and come in basically two types. An anvil pruner is inexpensive, and consists of a sharpened blade that cuts against a flat brass or aluminum plate. Using an anvil pruner will slightly crush the tip of the cut branch. The shear-type pruners are best, and a good pair will cost more than the anvil-type. Shear pruners provide two high quality steel blades and cut through a branch from both sides.
A pruning saw is ideal for cutting larger branches and getting into tight places. They generally have a wooden handle with an 8 to 15 inch curved saw blade. The teeth are wide set, with about six teeth per inch, to enable you to cut green wood easily without clogging with sawdust. You can use a firewood saw for large branches that are well spaced, but it is not meant for tight work and can damage the bark of adjacent branches.