It's summertime and I love wearing sleeveless shirts but I hate my fat, flabby arms! How can I get rid of them!?

diet and exercise.

You could add a weight routine. Some curls would help the upper arms. A lot of women fear the use of weights, but using light weights for arm strength and toning won't make a woman have bulky muscles. My arm muscles are pretty good because I carry around a 25 pound child all day The heaviest weights I use are 15 pounds (except my daughter.)

Also, add cardio to your excercise routine. That'll help with the excess fat.

A possible diet: a bowl of Special K cereal for breakfast, a jelly sandwich with trans-fat free bread and an apple for lunch, salmon and green-beans for dinner. Snacks can include carrots, celery or a banana.
Find snacks that you love that are healthy
Don't shop when you are hungry.
Add good fats to your diet.
Increase your daily fibre intake.
Try a daily walk.
Do strength training to build lean muscle.
Add one or two extra vegetables to your evening meal
Use a smaller plate
Avoid second helpings
Avoid/limit alcohol (3-4 standard drinks/week)- it reduces you ability to lose fat as well as making it harder to resist temptation.
Find a friend who wants to feel better too and use each other for support.
Listen to slow music while you eat. It's been proven to help you eat slower, which helps you lose weight.

Your first mission, should you choose to accept it, is to reduce the body fat.
Second, in order for that area of your arm to become tone, you'll want to build muscle in the back of the arm. That is called the Tricep and there's several good exercise you can do to build up that area.
But first, let me give you a list of some of the best exercises for flabby arms that will focus on the tricep and help you develop the area and make it stronger. This isn't all inclusive but it's some of the more common and better exercises you can do for the back of the arms.
* Weighted dips * Close grip bench press * Close grip push ups * Lying barbell French press * Overhead cable extensions * Cable press downs * Reverse cable press downs