Here are some generally cool ideas to get you started...
Put your weight on the outside pedal when cornering. Making a long, sweeping left turn? Put the right pedal down and place your weight on it. This will help your tires grip the turn, counter balance your steering and free up your inside foot for stabilizing (if you're a mountain biker). This tip would be used in a downhill turn when you're not spinning while turning.
Hold on loosely. Don't give your handlebar the death grip, especially on gnarly descents. Keep your fingers firmly around the grips, but with a bit of breathing room. The bike will actually track better and you won't get carpal tunnel syndrome.
Don't wear underwear under your lycra shorts. Cycling shorts (the kind with chamois padding) were made to be worn au natural. They're more comfortable and will keep you drier over the long haul. Downside for guys? You face potential problems if you see a hottie on the trail.
Buy new tires. This is a small cash outlay with big returns. A $30-$60 investment will make your bike ride so much better, and if you're a mountain biker, you'll look for loose rocks, hills and small children to ride over. Tires wear out faster than you think, and new rubber makes your rig look cool. Shop carefully, though; some bike tires cost more than car tires!
Go clipless. If you're even semi-serious about your riding, you'll want to get clipless, click-in pedals. The chief advantage of these snappy nubs is improved climbing. Because you can "pull" the pedal up as you mash it down on the other side of the crank, you'll be able to spin up hills better. Mountain Bikers: You'll also have more control in the rough stuff, since you won't be falling off your pedals as you deftly hop water bars and rocks. Bonus: jumping's a snap when you're clipped in.
Look where you want to go.
Mountain Bikers: If you look between two rocks on the trail, that's where you'll go--between them. If you focus on a big boulder during a descent, you'll hit it. Simple as that.
Roadies: Yes, your neck does get sore while your holding it up over a long ride while you're in the drops or on the hoods...but you can massage it out later which a lot less trouble than dealing with crashing into a stopped/park car, hitting a dog or even another biker. If you're in a paceline, do not focus intently on the wheel in front of you. You'll become "hypnotized" and your reaction time will be diminished. Look two or three riders ahead of you and see where you're going and keep an eye on the tire in front to gauge your following distance.
Carry tools. You will break down sometime. It won't be fun if you're stranded sans tools, and your riding buddies will get tired of it after the first time. I'd recommend a patch kit, tube, levers, pump (or CO2) and a chain breaker.
Don't shift under loads. Put simply, don't shift gears while you're climbing or pedaling hard. It's tough on your chain and rear cogs, and you'll probably blow the shift. Try to pedal smoothly while shifting.
Stretch. Ride for a few minutes to warm up, then stop and stretch. Your muscles will get a more effective stretch when they are warmed up. Stretch your hamstrings, quads, calves and lower back. You'll be amazed at how much longer you can ride in comfort when you're all loosey goosey.
Sit down during climbs. This one's a bit controversial, since some very good riders like to hammer out of the saddle on the climb. But generally speaking, you should sit 'n' spin. Find a gear low enough to let you sit, scoot forward and crank away. You'll save energy and have more steam in the long run.
Mountain Bikers: Scoot to the front of saddle when climbing. It sounds painful, but if you jam the front of your saddle between your cheeks on steep climbs, you'll improve your legs' power. You'll also weight the handlebar, preventing unwanted wheelie action.
Take baby steps. This is the best way to improve without becoming discouraged. In a race, don't try to win the first time out. First finish, then much later you can finish first. When riding, look for incremental improvement. Did you climb that hill in one bigger gear? Did you come down it with a faster max speed? Good job; now go hit the showers.
Train with better riders than you. You're not going to improve if you're the best rider in the group. You need to be pushed and dragged up the hill, hanging on for dear life. This will accelerate your fitness and make your friends feel really strong. But remember--once you get fit, it will be your turn to drag some lardass up the hill. It's climbing karma.
Ride in the rain and/or snow. Inclement weather will make you ride better. Wet surfaces force you to learn better how to control your bike so when you're riding this summer and hit that sandy spot, you'll know how to react.
Mountain Bikers: Trying to stay upright on snotty mud--or keeping traction in the snow-- will vastly improve your handling skills. So go jump over (or in) a creek and feel the wetness.
Use biking as a pickup line. If you do, you'll eventually meet people who like to cycle and/or mountain bike, and who won't distract you from your training. Then you'll be a better rider and enjoy the bonus of having sex in strange hillside settings.
Know how to fall. No problem there, eh? Seriously, if you're about to stack, roll or have a yard sale, do it with poise. Tuck and roll onto your shoulder. DON'T put out your hands to break your fall. It doesn't have to hurt...well, maybe it does. Learning how to fall is a good idea for roadies and a REALLY good idea for mountain bikers! (If you mountain bike, you KNOW what I mean.)
Don't obsess about your bike's weight. I've always believed that the best way to lift five crucial pounds from your bike is to lose the weight yourself. Get off the couch and go ride--you'll be surprised how light your bike gets and how much faster it'll go uphill. Tinkering with the weight of your bike is most effectively done after you've achieved your top performance in your own body. And when I say tinker, I mean like when you're considering buying those lighter pedals for $180 because their titanium hollow core spindles will save you 80 grams!
Ride, it's worth mentioning again! Nothing will develop your skill, endurance and cardiovascular fitness more than puttin' on the miles. Do it on the road, trail or in a spinning class, but get those legs moving. You'll find yourself admiring your svelte body in the mirror like some wacked-out Special K commercial in no time.