Please don't get into this elliptical bullshit. Elliptical machines give the illusion of a work out, when in fact they are nothing but momentum-producing-machines.
If you're just starting out, you're best bet is to join a gym. Taking membership at a place where others are working out, will both galvanize you, and keep you focused in the long term.
I suggest starting out on the stationary bike- 15mins. at a comfortable pace, followed by free-arm push ups, ab squats, light weights, etc. You should be done and out of the gym in 30 mins.- for a week or two weeks.
Over the next week and the next, you should build up to interval training <that is, mins. of max. exertion, followed by moderate, or aerobic, exertion> on the treadmill and stationary bike. You should be movin on to weight machines, preferably Nautilus, and doing 8 sets for time across various body parts after a 15 min. aerobic/anaerobic cardiovascular workout on the treadmill or stationary bike.
This is how you should be doin' it. Without the resting of the weight stack in between:
8 sets in 15 mins. tops. Ideally, with a weight, developing 8-10 reps. No resting in between sets. No repeating the same exercise. Repeat the movement to failure: which is, muscle fatigue- the point at which your arm / leg twitches and you can no longer move the weight stack.
I also recommend drinking a Whey based protein shake. You'll need it.
Build up to it. You won't get there in 2 or 3 weeks, or even months. You know you've done well, when you walk out of the gym nauseous and exhausted. Work out 3 times a week, with a gap of a day in between, and on your gap days do something light, like a 30 min. jog down the street or in a park. I highly recommend yoga for flexibility.
Believe it or not, anaerobic exercise- forms of exercise in which you work out intensely for short periods- are the best forms of losing weight. And there is no better form of exercise than that putting intensity on your muscles*.
If you can do a 'challenging' weight, a weight that you could ordinarily keep 10 reps of in your normal fashion, in that way in 6 months, you're gettin' good.
I'm willing to help you out on a weekly basis, if you want any assistance with forms, weights or even formulating an exercise plan.
I recommend the elliptical for pregnant women, war widows and the like. Not something you wanna get into.
Buy the book
'Nautilus Advanced Bodybuilding Techniques'. It's an investment you won't regret.
* Remember: Intensity and form is the name of this game. Take a day, or two, or three, to familiarize yourself with how to do the exercises properly. Your best bet is youtube: just type in the name of the exercise you see in the gym, and watch the videos that result. You'll get the general idea.
For the scientific-basis, of why I recommend Nautilus machines, and this intensity of workout, read the book.
Eventually, you should build your way upto something like this, which is a whole different kind of workout:
http://www.crossfit.com/
It is something I hope to introduce into the Indian Army, if ever I do get there.