You need to equip your player with clubs and balls bought in the Pro Shop. To do this you will use the My Equipment tool within the game. To access this tool you must be logged in to the game. Click on the My Equipment option under My Settings from the Main Menu. Additionally, you can access My Equipment immediately after you purchase a club in the Pro Shop by following the links on your Purchase Confirmation page or by clicking the View/Edit Equipment button prior to teeing off. My Equipment can also be accessed in the Change Club pop-up by clicking the Club Selection button, however changes cannot be saved while a game is in progress.
Once you are in the My Equipment interface you need to "click and drag" the club or ball you would like to equip from the inventory section into the In My Bag section. Make sure you click the Save Changes button.
Click here to view a tutorial on equipping your items.