Summarize:

Pay attention to your surroundings and take care to stay out of any blind spots on the road. Avoid weaving through traffic, or riding on the shoulders.  Drivers should be keeping an eye out for bikers, but do your best to make yourself visible on the road. For extra safety, always assume that you're invisible to other drivers.  Always follow the local traffic laws. Don't speed, and always keep an eye on the traffic ahead of you. You should never ride your motorcycle without wearing the appropriate safety gear. Even if you're going down the street, wear your helmet. Handling a motorcycle requires more skill than driving a car. Drinking before riding your motorcycle will hinder your ability to ride safely. Don't be fooled into thinking that you can ride if you've only had a few drinks. If you have a bike that allows you to carry a passenger, make sure you are skilled enough to carry them on your bike. Give your passenger a helmet, and make sure they're comfortable riding with you.
Be courteous to other riders and drivers. Always wear your safety gear. Ride sober. Take extra care when riding with a passenger.