you have to cut the alcohol and soda, atleast until you have reached your goal weight. Eating vegetables and fruits is great for nutrients but the sugar will keep you at your maintained weight unless you work out.
Your 19 so your metobolism should be great. The main thing your going to want to work on is your muscles. Full body work-out is truly the way to go. The upper body today and the lower body tommorow myth is just that, a myth. The more of your body that works out in a single session the more calories you will burn after you have been done working out.

What can I do when I work out/exercise to lose my belly and help shape out my pecs?

The best thing for your belly is situps. The way i do them is cup my ears with my hands. Lift my legs and the lift my butt off the floor with my stomach muscles. It hurts but, you will feel it. Learn to love the pain, it'd be easier for you.
For your pecs, you should do tons of pushups and diamond pushups. Lifting weights helps, the rule for lifting is to lift as much to do 8 reps easy, but not able to lift after 12.
you should alternate each day. one run for 30 minutes and the next day full body workout.
As far as running is concerned you should do speed intervals, run as fast as you can, then jog and keep repeating the process for 30 minutes. It will burn a lot more calories in 30 minutes as regular jogging will.
Things to eat:
Almonds and other nuts
Beans and other Legumes (including soybeans, chickpeas, pinto beans, navy beans, kidney beans, lima beans)
Spinach and other green veggies
Dairy Products (fat-free or low-lat milk, yogurt,
cheese, cottage cheese)
Oatmeal
Eggs
Turkey and other lean meats
Peanut Butter (natural)
Olive Oil
Whole grain Breads
Extra Protien (whey) powder
Raspberries and other berries
taken from the abs diet by David Zinczecko

This week I kind of messed up, i'm starting over next Monday.

Do you think if I keep it up for 5 days a week at 30 minutes a day I will see a difference in 1 month?

5 days a week 30 minutes a day...Yeah I think you will see a differance in a month... You got to keep your diet reasonable though...If you are 19 and gaining weight so easily, I think you are going to have a constant battle with weight. You had better get some good eating habits because it will be especially important in your case.

in my oppion i think running is the best thing maybe to start try running a mile evry day even if your slow at it you will burn thoes cals. then one you get better try to increse my aunt did it and now she ways less then me.. good luck

Here's the deal, I have actually managed to build up a 6 pack and here is what I know from experience, not some cheesy ab program ad.

2 parts of ab tone:
#1 Abdominal exercises, focus on lower back (bicycle situps will work them), obliques (side situps), upper abs (normal situps), lower abs (leg lifts) to get a holistic ab workout, you only need to do about 40 reps per exercise since abs are mostly fast-twitch muscles
#2 Aerobic exercise to actually burn off the fat on your abs-Your body loses fat equally, situps won't specifically burn belly fat, try jogging (maybe working up to 1 mile without stopping or 2 miles if your looking for a challenge)