Like the other members said, the key to getting rid of that fat is cardio exercise. You can do this using the machines at the gym, or even doing group fitness classes, which are a lot more fun. The main thing is that you have to be consistent with exercise. Because it is about calories in versus calories out, you need to make sure that you are burning up more calories than you are eating in order to lose the fat.
When you first start out you will probably find that the weight loss is relatively easy, especially if you have not been exercising on a regular basis. So to start with 5 days of cardio and endurance style strength training would be idea. Unfortunately you can't spot reduce, so you will have to lose fat overall in order to make those stubborn areas smaller too.
Muscle is your friend, the more muscle you have the more calories your body will burn even when you are not doing anything. Women can't really build bulky muscle unless you are pumping really heavy weights, taking steroids or are naturally very muscular. I highly recommend circuit style workouts where you alternate between cardio and weights, this keeps your heart rate high and is also fun to do.
In terms of working out at home, I would suggest getting yourself some workout DVDs. There are thousands to choose from and they are so much more fun than trying to come up with exercises yourself. Jillian Michaels and Bob Harper have some awesome workout DVDs. If you google workout DVDs for hips and thighs there will be many options. Amazon has a great range and usually has heaps of reviews to help you choose.
You might also want to use an online calorie calculator to work out how many calories you should be eating to lose weight. Just being aware of the amount of calories in the foods you commonly eat will help you to make wiser choices. You don't necessarily have to count everything, but just get a general idea.