How to know if a tree is dying

Knowing what to look for when looking at your trees is important. You can see signs of a dying tree in the leaves, branches, bark and trunk.
Deciduous trees, which lose all their leaves each winter, have most signs in common with evergreen trees, which never lose all their leaves at once. Deciduous trees may drop their leaves during the growing season if they are dying. If the leaves turn brown and brittle during the growing season, the tree may be dying. Yellow leaves on a tree that usually has green leaves are also a sign of a problem.
Evergreen trees will start to show red or brown needles. Once the top third of the plant has needles that are red or brown, the tree is definitely dying. Trees showing yellow needles are stressed and may be dying.
Look for holes, cracks and peeling bark. Bark will become loose and start falling off a dying tree. It may sport fungus or holes where wood-boring insects like Termites, Wood Cockroach or Paloverde Root Borer have made homes in it. Brittle bark is also a bad sign. Bark beetles indicate dying bark. Places that are bare of bark are a sign of problems, this means that side of the tree is not getting any nutrients. Carpenter ants are a sign of deadwood. Rows of holes from boring insects are also a sign that the tree is in trouble. Fungus on the trunk is a sign of dead and decaying wood.

Fungus may grow on dead branches. It only grows on decaying wood, so whatever portion of the branch it is on is dead. Wood boring insects will also move in when a tree is dying. Branches start showing holes where the insects have made homes or bored holes to eat the wood.

Here is a great website on Signs of a dying tree:
http://www.gardeningknowhow.com/ornamental/trees/tgen/what-does-a-dying-tree-look-like-signs-that-a-tree-is-dying.htm