I'm a Certified Fitness Trainer through the International Sports Science Association (ISSA), and am currently working on their Sports Fitness Nutrition course (I've been slacking a bit lately, though).
Diet is key. People can lose weight with just a diet, but if you exercise and splurge on calories you won't lose body weight. Also, try not to think of it as "losing weight," rather, think of it as "losing fat" since you can always gain muscle mass.
While jogging is better than no exercise, I highly suggest getting into anaerobic activities such as weight-lifting or even sprints. With weight-lifting, for example, you'll increase your metabolism when you have more muscle, as well as your strength as your body adapts. Does this mean you have to go out today and buy a bench press and a ton of weights? No! You can start with calisthenics, or using your own body as a weight. For example, push-ups and pull-ups. Isometric exercises such as Planks and Bird-Dogs are great for your core. Ensure to take in an adequate amount of protein (Many state that it's about 1g per lb. of body Lean Body Mass), but it could vary depending on your goals. If you go to a gym, work on compound lifts (Exercises that use more than one muscle group) such as Pull-Ups, Bench Press, Deadlifts, Squats, and so on.
For losing body fat, you need a caloric deficit. Cut around 3,500 calories per *WEEK* from your caloric intake and exercise and you can drop 1-2 lbs. per week. Cut out the candy, burgers and other junk food. Spit out the soda! Ditch the simple carbohydrates such as white bread, white rice and generic pasta! BAD! It not only will convert to fat if unused and stored for future use if you don't exercise, it takes a toll on your blood sugar levels. You need complex carbohydrates (Google it for a list!) for more sustainable energy. Vegetables will be your best friend for losing body fat since they are low in calories, yet high in micronutrients (Vitamins, Minerals). Drink water and tea.
Another facet is supplementation, which you can purchase. I take Fish Oil every day (They're Omega-3 fats) and such. I also have a protein powder to help ensure I meet my daily requirement for protein (I mix it in Almond Milk).
You can PM me with any questions!