After a storm large trees may have split branches. Making the proper pruning cuts is critical to safety of the person pruning and for the long term healing for the tree.

Making the Cut
Successful pruning requires that all cuts be made in a way that allows the plant to close off the wounds and resume healthy growth. Always use the right tool for the job, and make sure it is clean and sharp. Prune at the proper time of year and follow the pruning techniques appropriate to the plants response potential and the desired outcome.

When heading back a small branch to a healthy bud, do not leave a stub which will be unsightly and may serve as an infection site. On the other hand, do not prune so close the the bud that is is damaged. Generally, a slightly angled cut about 1/4 inch beyond the bud  is appropriate.
Before thinning out a branch, look closely at its structure. You will recognize the branch collar, a slight swollen area at the base of the lower side of the branch, and the bark ridge, a V shaped region in the top angle between the branch and the main stem to which it is attached. Both the branch collar and the bark ridge must remain intact after the branch is removed, in order for the plant to close off the wound successfully. Never make a flush cut. Rather, locate the branch collar and the bark ridge, and angle your cut appropriately to cut just beyond them. The angle of your cut will depend on the species of plant, as the size and shape of the branch collar and bark ridge very from species to species.

Branches large enough to be removed with a pruning saw should be removed with three cuts because their bark may tear if they are removed in one step, causing irreparable damage. First cut upward halfway into the branch, one to two feet away from the final cut. Second, cut downward into the branch one inch out from the first cut. This will remove most of the branch. Third, make the final cut based on the location of the branch collar and bark ridge.

Tree paints and wound dressings should rarely, if ever be used by a homeowner. Recent research has shown that these materials are rarely beneficial. In fact, they may sometimes prevent plants from closing off wounds. Sometimes arborists will use wound dressings if they are pruning at a time of year when a specific insect or disease organism is active. If in doubt consult a professional.