First, you must remember that safe, steady weight loss takes time. Don't be fooled by the '30 day' crash diets you see advertised on TV, most people give up on these as being too extreme to follow, or just revert back to bad habits once the diet is over.
I used to be fat, but I lost weight through extra walking. After a few weeks of walking an extra 30 to 60 minutes a day,
I was losing weight quite steadily, especially as I'd reduced my intake of high fat or high in sugar foods like chips and candy bars, eating maybe one a week as a treat instead of one a day out of habit.
If you take up walking, after a while you'll find you can walk further and faster, and this will act as encouragement to stick with the diet. Once you've lost sufficient weight, you'll feel more up to more vigorous exercise such as running (just 10 minutes a day is enough to get you started), or joining in with a team sport. Personally, I wouldn't bother signing up to a gym unless you're serious about bodybuilding. Most of the really beneficial exercises can be done at home or in the park.
As for diet, I always go by the fat content of food, rather than calories, although the two often go hand-in-hand. Always keep nutrition in mind, a diet should not mean starving the body of the goodness it needs. Remember - there's no such thing as junk food, only junk diets.
One more tip - weigh yourself only once a month, perhaps once every 2 weeks if you're getting started, that way you'll
notice the difference more and will be less inclined to give up.
Dancing is a fun way to exercise and can be done at home on your own, so slip on a comfortable t-shirt and join in with this YouTube video: