Yes, unfortunately spot reducing doesn't work, so you will have to lose fat in general for your arms to become smaller. The best way to lose at is through good nutrition and interval training, which is a combination of weights and cardio. The weights will increase the amount of lean muscle you have, which in turn will help increase your metabolism to shed fat, and the cardio will keep your heart rate high and burn calories. The main key to weight loss is calories in versus calories out. You need to be eating less than you are burning.
There are many ways to exercise at home, if you don't want to hit the gym. You can either do your own circuit style training using pure body weight exercises, or you can get some equipment like dumbbells, a resistance band and something you can use as a bench, so that you can get into some proper weight training. A lot of women think that weight training will just make them look even bigger, but the fact is that muscle is a lot denser than fat and therefore takes up less space. If you lose the fat on top of the muscle through diet and cardio, then increasing your lean muscle mass will give you a shaplier, more toned appearance.
If you are unfamiliar with what sort of exercises to do then you could try buying a few workout DVDs. There are so many great ones for shedding fat and toning the upper body specifically. The Firm has a huge selection of DVDs that use the interval training principle for maximum results. Also the 10 minute solution series is great because it has all different workouts broken into 10 minute segments so that you can either do them all together or separately, depending on how much time you have. I swear by workout DVDs. It means you have no excuses cause you don't even have to leave the house. No expensive gym fees and minimal equipment (you can even fill water bottles with sand for hand weights).
If you don't like the idea of workout DVDs, however, you could simply google "body weight exercises" or "equipmentless training" and there will be a whole bunch of sites giving you ideas on what exercises to do.