How to select an arborist
One of the best ways to select an arborist is to ask to see his work. It only takes a half hour, and if the tree is in your yard, you may be living with his work for years.
The most common abuse of a tree is a practice called "topping" in which the outer part of the branches is cut off. This has several bad effects. It deprives the tree of leaves, starving it and making it more susceptible to insects and fungi. Since most of a branch is intact, the sap continues to flow to the end of the branch, encouraging new growth to be small, weak bushy sprouts at the end of the cut branches. The new weak branches shade each other and are ugly.
Branches should be removed so that relatively few, large branches remain. The branches that remain should retain most of their leaves. Ideally, the tree will be shaped away from wires, buildings and human spaces. It should become more open and yet remain natural-looking.
Finally, most of the "arborists" that are unskilled-enough to top a tree, also fail to protect the heartwood with paint or pitch. Most often they leave it exposed to rain, rot and boring insects.
Correct trimming removes smaller branches near the trunk. A cut should be made vertically or be slightly overhung to keep water out of the heartwood. Bare heartwood should be painted to discourage insects and rot. The paint is more critical as the cut is closer to the trunk, and heartwood or the climate is more wet. Some trees have wet heartwood, and a cut must be painted or pitched.
A professional arborist will not leave branches on the ground, to be a safety hazard or nuisance. If he cuts down a tree, he will know how to remove stumps. He will also have a truck with a chipper, and clean up after himself.
Lastly, be sure to ask if the arborist carries insurance. In some jurisdictions, unless you make other arrangements, as his employer you will be responsible for his care if he has an accident while climbing your tree. If he is going to remove a tree near a building, be sure he is bonded.