Where to cut a small woody branch
When removing a whole branch, keep the swollen collar at its base.

Before you start
Look for a slight ridge or swelling where the branch meets the trunk or parent stem. This is the branch collar. Make sure the branch is small and easy to reach from the ground.
How to do it
For a small branch you can cut cleanly with hand pruners, cut just outside the collar, on the branch side. Keep the collar intact and avoid leaving a long stub.
When to stop and recheck
Stop if you cannot see the collar, the branch is heavy or overhead, or you would need a ladder. Get an arborist's help for branches you cannot remove safely from the ground.