First thing, get a heart rate monitor. You need to know what is going on with your body.

Think intervals to get faster. You need to train your body to use fuel at higher heart rates. Intervals are taxing, however, so you only want to do them once or twice a week if you are not in good shape.

Base miles for longer rides are important. You would keep your heart rate at ~ 65% and just aim to get miles in. You would do this once a week.

Weight training is good for getting your body stronger. You'll be frozen in the same position (essentially) for awhile. Additionally, strong legs make sprinting and hills easier. Squats are good all around leg exercises. Get a good book or personal trainer to help you in the weight room. You'll taper off of weights as your rides get longer. Don't neglect your upper body. Your triceps get a workout and your lower back is very important.