Visit the nearest ski supply store and purchase a pair of new ski baskets. It is always a good idea to replace both baskets even if only one is damaged. Ski poles baskets are fairly inexpensive.
You will need a friend to help you out. Ask your friend to hold the pole with the damaged or broken basket firmly in order to prevent it from moving while you will be replacing the basket in the steps to come.
Place a crescent wrench of variable width on top of the ski basket you are trying to replace. Slowly tighten the wrench until its width is only a tiny bit more than width of the ski pole.
In order to remove the old basket, strike the wrench handle as close to the ski pole as possible with a rubber mallet. This will create a fair amount of impact force so ask your friend to hold the ski poles firmly before whacking the wrench. Three to four rubber mallet strikes and the basket will slide off nice and easy.
Rotate the ski pole such that the basket side of the pole points towards the sky. Ease the new basket carefully into place.
Keeping the pole upside down, place the crescent wrench right on top of the new basket, just like you did in the third step. Unlike before when you actually whacked the wrench, you will now need to gently tap in only with a rubber mallet. Continue until the replacement basket is snug with the pole and does not move or rotate in any way.