Strength training to tone the upper arms, along with proper nutrition to reduce bodyfat, will make your arms smaller as muscle takes up less space then fat. The triceps, the muscles on the back of the upper arm, account for 2/3 of the size of the arm. Training them will get your arms toned quickly. (Who wants the underside of their arms to continue waving after they’ve stopped waving?!)
For those of you just starting out I would recommend performing countertop push-ups. Push-ups with your hands on a countertop with your feet 2-3 ft from the countertop – depending on your height. The countertop should touch the bottom of the sternum. Once you can perform 3 sets of 10-12 reps you can progress to knee push-ups and then toe push-ups. Good luck!