How can I get results like this in 2 months?

If you want to lose fat, you have to be in a calorie deficit. Your body won't access stored fat until it needs that fuel because you haven't eaten enough. If you want to lose, say 5-7 pounds of fat, eat a high-nutrient, low-carb diet with a 500 calorie a day deficit -- and make sure you getting plenty of protein because...

To get a more defined and flat mid-section, you'll need to work out.  There are hundreds of free YouTube videos for full-body/body weight programs as well as ones that focus on the core. Aerobics/cardio will help improve your cardiovascular endurance and burn calories.  Sit-ups, dips, push ups, leg lifts, squats, lunges, and other "weight bearing" exercises will help tone your muscles.

If you lose fat and gain muscle, your weight should stay close the the same but your body composition will change.

The other things you see in picture #2 ("after') like the thigh gap, are due to changes in how the woman's body is positioned, camera angle, and photo shop. 

Start with brisk walks, and graduate to running.  This is a great way to get cardio and the advantages of being outside.  At home, you can do crunches, push ups and the like.  Find some Youtube videos that are specifically for body weight exercises.  Yoga by Adrienne is a Youtube channel that's obviously all yoga.  But she does have some routines for weight loss that are all-body exercises.

Anything that improves your posture will help.

Almost all of your 'fat' in the midsection, resulting in a tummy bulge, is due to the curve in your spine.