Start walking on a treadmill or use a stair climber, or an elliptical machine, or a stationary bike. I would suggest you start out slow to prevent any injuries because if you get hurt while trying to increase your stamina you will not be able to keep working out and will have defeated the purpose of trying to lose weight. So, start slow and work up to being able to do thirty minutes of pretty intense cardio at least three times a week.
A HIIT session consists of a warm up period of exercise, followed by six to ten repetitions of high intensity exercise, separated by medium intensity exercise, and ending with a period of cool down exercise. The number of repetitions and length of each depends on the exercise. The goal is to do at least six cycles, and to have the entire HIIT session last at least fifteen minutes and not more than twenty.
HIIT is considered to be an excellent way to maximize a workout where time is limited.
Once you get your stamina built up using your stairmaster, you can pretty much handle anything from here on out so my suggestion would be to add some weights and strength training to your workout. The more muscle you have, the more fat you will burn all the time, not just when you work out.