Besides the only tried and true solutions to any and all fat loss - diet and exercise - there is the liposuction option. I don't recommend this radical solution. I know of way too many horror stories and have seen two really bad ones up close and personal YIKES!!! Not only is it extremely painful even well after the surgical "wounds" (mostly "holes" from the suction insertion) are healed but the skin can become discolored BLACK. Tissue necrosis(death) is horrible and happened to a friend of mine - not only unsightly but dangerous. I have my NANA's hanging arm fat no matter how skinny I get and no exercise in the world ever helped me reduce it even a bit. Just wear the right shirts unfortunately I can never go sleeve less if I care about who I'll be around but I don't care for tank tops anyway. T-shirts are nicer looking. Sorry I couldn't be of more help. Love yourself just as you are I'm sure those who matter to you DO and that's all that matters!
You lose arm fat just like you do other fat, cut back on calories. If you are eating fewer calories per day than your body burns then you will lose fat and eventually that includes the fat in your arms. Check out www,mypyramid.gov for more information on the type and amount of calories you should be eating daily in order to lose weight :)
Spot reduction is impossible. You should consider exercising or do a regular physical activity. Ever think about doing martial arts? I have a 3rd degree Black belt in taekwondo. That's how I stay in shape.