Hi kellamity - Zumba is a good start! Once you've built up a good base fitness have a look at spinning and Body Combat to vary things a bit.
Some ideas:
Low-carb/slow-carb is the most effective diet strategy to start burning fat quickly - cut out sugar, bread, pasta, potatoes, rice and compensate by eating more green veg, beans, dairy, meat, fish etc. Do not start messing around with "diet" foods and low-fat, low-calorie nonsense. You need to wean your body off carbohydrates and insulin and kick-start it into burning fat. It's also easy to deal with food cravings because you can just go and eat a mahoosive lump of cheese and still feel virtuous :)
Secondly - exercise is vital - and you need to approach this in two ways. Cardio training (e.g. zumba) will increase your overall fitness, metabolism, heart function etc - it will also burn off calories, decrease your blood pressure and generally make you healthier.
However, cardio is not generally enough to get 'fit' - you need to do strength training too. If your gym does Les Mills classes, then Body Pump is a good place to start, otherwise ask someone to show you a basic strength (weights) routine - start with the machines but you will probably want to progress to free weights as soon as your strength increases a bit.
Strength training has many benefits - putting on muscle mass not only makes you look great but muscle burns calories even when doing no work. You will also increase bone strength and density which is the best way of protecting against osteoporosis in later life. It's also great for posture and general neck/shoulder/back/hip/knee problems.
If you have very little time and don't manage to do any other exercise, you can do a tabata interval in 4 minutes flat! Again, you might want to build up your fitness a little before you attempt tabatas but they are very useful if you haven't managed to do your usual exercise.