One of the biggest mistakes that people make when they start biking is to take the exact same routes they used when they were driving. It's usually better to take the streets with fewer and slower cars. Sure, cyclists have a right to the road, but that's a small consolation when you're dead. Consider how far you can take this strategy: If you learn your routes well, you'll find that in many cities you can travel through neighbourhoods to get to most places, only crossing the busiest streets rather than  travelling on them. 

Assume that motorists don't know you're there and ride in such a way that they won't hit you even if they don't see you. You're not trying to BE invisible, you're trying to make it irrelevant whether cars see you or not. If you ride in such a way that a car has to see you to take action to avoid hitting you (e.g., by their slowing down or changing lanes), then that means they will definitely hit you if they don't see you! But if you stay out of their way, then you won't get hit even if they didn't notice you were there. 

On very fast roads, cars will have less time to see you because they're approaching you so fast. Now, you should avoid fast roads in the first place if at all possible, unless there's plenty of room for a  car and a bike side by side. And if there IS such room, then on fast roadways, you can practice invisibility by riding to the extreme left. If you're far enough left that you're not in the part of the lane the  cars are in, then they'll zoom by and won't hit you, even if they never saw you. (Exceptions to riding on the extreme left are noted below) 

Here's another example: It's a good idea to signal a right turn, but it's a better idea to make your right turn at a time or place where there aren't cars behind you that could hit you while you're stopped and waiting to make that turn. You can hang out in the middle of the street, stopped, with your right arm out, waiting to make your turn, but you're counting on cars behind you to see you and stop. If they don't see you, you're in trouble. 

Naturally we don't advocate running red lights, but if you're the kind of person who does, then apply the invisibility principle when deciding on whether to run a particular light: Could any cross traffic possibly hit me if I were invisible? If yes, then absolutely don't do it. Never make a car have to slow down to avoid hitting you (red light or not). Remember, the more you rely on cars to see you to avoid hitting you, the more chances they'll have to actually do so. 

Remember, you're not trying to BE invisible, you're just riding with the assumption that cars can't see you. Of course, you certainly WANT them to see you, and you should help them with that. That's why you'll wave to motorists whom you think might be about to pull out in front of you, and why you'll be lit up like a Christmas tree at night (front and rear lights). 

There are exceptions to riding as though you were invisible. For example, often you'll need to command a whole lane of traffic instead of riding to the extreme left, for the reasons mentioned in the next section. 

While you'll often prefer to ride to the extreme left to keep out of the way of cars passing you, it's often safest to take the whole lane, or at least move a little bit to the right. 

As you'll see from the diagram on the right, riding a bit to the right allows cars at cross streets at intersections to see you better. Also, you should take the lane if cars are passing you too closely from behind. This requires cars behind you to see you and either slow down or change lanes. Then again, if you're on the kind of street where you've got cars blocked up behind you or constantly changing lanes to get around you, you're probably on the wrong street and should find a quieter neighbourhood street. 

By the way, it's perfectly legal for you to take the lane. RTA (and the laws of most other states) says you have to ride as far to the left as is "practicable". Here are some things that make it impracticable to ride to the extreme left: 

If you're paying attention, you'll notice that there are risks to both riding to the extreme left as well as taking the lane. If you wanted a steadfast rule, then sorry, it isn't that simple. (But take heart, because many of the OTHER concepts we mention in our Top 10 list above work 100% of the time.) If you ride all the way to the left, you risk getting doored, and you make it hard for cars at cross streets at intersections to see you. But if you take the lane, you'll definitely get hit if a car behind you doesn't see you. To make it more likely that they'll see you when you're taking the lane, be lit up like a Christmas tree at night, and take neighbourhood streets when you can, since the cars will be travelling slower and therefore approach you from behind slower, and have more time to see you.