This page is for those just getting started in road biking. You probably have a lot of questions. I'll break those down into some basic categories and try to provide some simple advice.
You'll need a bicycle When you're just getting started, you may be hesitant to make a large investment. Don't worry, there are several options available. Many cyclists have more then one bike, so you may want to ask around about borrowing one. By the way, you can ride a mountain bike on the road, but you'll expend a lot more effort to go the same distance. A road bike, or even a "comfort" bike is usually a much better choice for the road. Perhaps you want to buy a used bike: Craigslist is a great source for used bikes. Garage sale bikes can be a great way to get started, but it might be a challenge to find one that fits. I suggest checking the local papers or Cycling Utah. When starting out you don't need to worry about clipless pedals or how much your frame weighs. Just get a bike you can ride.
A bike that fits will make all the difference in your comfort and enjoyment. The most basic measurement is the frame size, it's often specified in centimeters such as "54cm". Also, many bikes now use a Small, Medium or Large designation these days. The options can be dizzying, but the point is to get a bike that feels comfortable. There's a simple sizing formula here and great bike fit calculator here. You can ride a bike wearing shorts, but you'll probably find it uncomfortable after a while. Cycling shorts can help. Twenty dollar cotton spandex shorts with a chamois will do fine when you're ready to try them out. Mountain biking shorts aren't a bad idea if you want something that looks a little less serious.
Where to ride I suggest starting in your neighborhood. Seriously, take some time to get used to riding a bike again, it may have been a while. Get used to your brakes and shifter, starting and stopping. Start with rides a couple of miles long and take your time, you'll have vast confidence in no time. When you're feeling good, hit some of the local bike trails. Here are three that I suggest: the Draper rail trail, the Sandy Trax bike trail and the Jordan River Parkway. When you're ready to start riding on the road, start with routes that have a wide shoulder, and remember, you have all the same rights and responsibilities as the driver of a car. Obey all traffic rules. Sidewalks are for pedestrians and cyclists are not pedestrians (despite what you may have been told as a child).
What's next Now that you have your confidence built up and some miles on your legs, there's two places to go: longer rides and hill climbing. Here in Salt Lake, longer rides mean heading north and south. Hill climbing means going east. Take a look at the other rides profiled here and pay special attention to the altitude profiles and total elevation numbers. Many riders find it fun to hit the road with other cyclists. An easy way to hook up with others of your skill level is the group rides section of Cycling Utah.
My most important advice is to be safe and have fun.