Cardio (your jogging) should be at least 20-30 minutes, but you may need to work up to that. That's about how long it takes for your body to move from burning carbohydrate stores to using fat stores.
Unlike with cardio exercise, weight training will help you burn calories on more of a 24x7 basis. It's thought that this is partly because lean muscle consumes more calories than fat stores, so build up that lean muscle. Start with exercises that work your biggest muscle groups: chest, back, shoulders, and legs. Start with 1 or 2 different exercises, 3 sets per exercise, and 12-15 reps per set. Be sure to go as close to muscle failure as possible.
As far as frequency, I'd say you'll want to work into it. Start with 2-3 days/week of jogging, 2-3 days/week of weights. Could even be done on the same day, in which case I'd jog first to get your body warmed up for the weights. If you start too fast you might burn out and find adherance to the routine to be a problem.
You should see results within the first couple weeks, but be prepared for peaks and valleys in your results. Long term consistency is the key.
Don't restrict your diet too much, or your body will go into starvation mode and not burn the calories you want it to. Eat plenty of fruits, veggies, whole grains, lean meats, fish (fatty fish is good for you), and healthy sources of fat like nuts, seeds, and avocados. And don't totally deprive yourself of desserts and treats, or again adherance might be a problem.
Finally, I'd take think about finding a good protein drink to supplement. Whey protein is efficient and fairly inexpensive. Most supplements are a waste of money, or at best only minimally beneficial.
Bob
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