Wrap wire tightly around diameter of foam ball once. Twist wire at top of ball to secure. Tuck ends into ball.
Break toothpicks in half. Push cranberry onto broken end of toothpick; push other end of toothpick into foam ball. Continue until ball is well filled with cranberries.
Fill in open spaces on ball with 1 1/2- to 2-inch cuts of eucalyptus, securing with pins.
Slip ribbon through wire twist at top; tie ribbon to make loop for hanging ball. The cranberries will stay plump and pretty for about three to four days. To extend its life, hang the ball in a cool spot, such as in an entryway or on a porch.