Step 1: Preparing your bike...
Alwayts make sure to get a tune-up every once in a while. Lie your bike down on its side. Spin both wheels, and make sure there is no scraping sound. This means your brakes are too tight, which may slow you down significantly. Also oil your bike occasionally, you don't need to do it that much. DO NOT USE WD-40 ON YOUR BIKE CHAIN!!! THAT WILL DAMAGE IT!!! Just buy a small bottle of bike oil from a local shop.
Ok, now that's over with.
Step 2: Clothes to wear!
Step 3: Biking!
Do not coast. Pedal! Even when you are going down hills, PEDAL!
Ok, I hope that was emphasized enough.
Also, bike at least a few days a week. If you don't have a gear bike (I hope you do), get one. If you are pedaling and your speed is not increasing, get a bike with more gears. I recommend a 21 speed bike, if not more. Use the highest gear whenever possible, even when going up hills. This is difficult to achieve, but with practice, biking quickly up steep hills becomes much easier. Also, bike using a route that gives you time to pick up speed before going up hills. But when biking fast, remember to brake! I know when speeding down a hill at 35 mph, you don't want to stop at the stop sign or traffic light ahead. But you could get seriously injured if a car is coming, or lose serious cash if a cop is near. Also, always bike on the right side of the road (in the U.S.) to best avoid collisions. To increase speed before going up a hill, stand up on your bike at your highest speed. This allows you to bike easily up steep hills. Also, I've done some tests with some of my friends. We noted that the higher the seat, the faster you bike (well, as long as you can still touch the ground). A good height is to have your feet just touching the ground. This is crucial when you are stopped at a red light or at a stop sign. It is good to pedal with the balls of your feet, also. Don't pedal with your heels. I know it seems difficult to ride up hills on high gears, but with practice, it increases the speed greatly.
The image below is of my bike. Well, that's not my bike, but it is the same type and all. A good bike at not a bad price, the cost was under $300.