Cut a length of nylon string for each gazing ball. The string should be between 12 and 18 inches. Too short a string will prevent the ball from swaying in the breeze; too long a string could encourage the sphere to sway too much and smash into the closest structure.
Tie the a string firmly to the stem of each gazing ball. Thread the string through the loop, tie it and then tie it again, pulling it as tight as you can. Tie the other end of each string to a steel hook using the same method.
Place a screw in each place you plan to hang a sphere, leaving about 2 inches of screw sticking out of the surface. Choose places partially shielded from foul weather at least 6 feet off the ground. Use screws even on trees; the screw hurts the tree less than wrapping something around its limbs that may choke the branch as it grows.
Space the balls at least 2 feet away from each other to prevent collisions. If using a ladder to reach any of these places, have a friend hold it steady for you
Slip the hook of each gazing ball over its own screw. Push the gazing balls to make sure they won't hit anything in a high wind.