Congratulations on your resolution! I suspect that once you get going and get your system figured out, you may well find that it makes lots of things about city living much more convenient.

The best thing you can do to start with, if you're nervous about riding in traffic, is to read up on the specific laws relating to bikes in your area, and also on some general good advice for riding in traffic. There are lots of good sites for this, such as the League of American Bicyclists and whatever advocacy organizations are local to your area. Also, look up John Allen's Home Office Home Page for an in-depth pamphlet called "Bicycling Street Smarts" (which you can read on the site for free) for specific stuff about how to handle specific maneuvers like left turns, traffic circles, etc. Another good site is Bikeyface which is a webcomic about biking in the city and has cute, funny cartoons with sensible, down-to-earth advice.

But in a nutshell, the first rule is to obey the rules of the road. You're a vehicle too, so stop for stop signs and red lights, etc. Always ride on the right side of the road (unless you live in one of those countries where they drive on the left) and don't go the wrong way down one-way streets. Ride defensively. Use hand signals to make your intentions clear, especially when turning left or changing lanes, and ride predictably.

Some of the most common and easily minimized types of urban bike-car collisions (aside from going against a one-way street) are car doors, "right hooks", "left hooks", and getting t-boned at driveways. To avoid car doors and driveways, make sure that you always ride a safe distance from parked cars. That should also give you and anyone pulling out of a driveway enough time to see each other. If you're hugging the right side of the road, you're not only in the door zone, but you're also effectively invisible to anyone pulling out of a driveway or even stepping off the curb to get into a car.
"Right hooks" are when you're on the right side of the road (even in a bike lane) and a car on your left decides to turn right. You'd be surprised at the number of people who have had every opportunity to see you while they were overtaking you from behind, but turn right across your path anyway because it just didn't occur to them to put those two things together. So if you're approaching intersections where people can turn right, get in the middle of the right lane if you can. Watch for which direction wheels and heads are going, because people don't always use their turn signals.
"Left hooks" are when you're going straight and someone coming the opposite direction turns left and hits you in the middle of the intersection. That may be because they thought thhey saw a gap in traffic and decided to scoot through it, only it was someone on a bike instead. To avoid this, try to position yourself so you can see oncoming traffic; don't tailgate the righthand corner of a large vehicle, because someone coming the other way won't see you.

Always use a red tail light and a white, non-blinking headlight when riding at night. Keep in mind that while lots of people like blinking lights under the rationale that they get attention, humans also have more trouble judging the distance and speed of blinking lights, so using a steady one as well is a good idea. Especially with some of the extra-bright headlights, sometimes a blinking headlight looks like it's farther away than it really is. Needless to say, that's not a good thing. Reflective gear is a good idea, too. It doesn't have to be a vest that makes you look like you work for the highway dept, but keep in mind that surface area is what counts and you want to be visible. So don't go riding a black bike in black clothes in a dark neighborhood.

You might consider looking into the classes that the Bike League offers ("Traffic 101" I believe) or other programs in your area.

Good luck, and have fun!