When you get caught in the rain, getting out safely is your first priority. The most important thing to remember is that water will get everywhere, and thus, it'll reduce traction everywhere. When your tires get wet, they're less able to grip the road. Sopping wet brakes have almost no friction and take much longer to stop you. Even your seat and handlebars will be dangerously slippery. When you understand why a bike is much harder to control in the rain, it'll be easier to remember why you need to slow down.
Put simply, keep in mind that everything takes longer. It might be tempting to pedal as fast as possible to get home more quickly, but resist the urge. Keep a comfortable pace so you have adequate time to see and cope with hazards (remember, your visibility is also impaired), and anticipate when you'll need to slow down. Squeeze the brakes gently long before you actually need to slow or stop; this will purge excess water from your brake pads and rims to provide you with some grip. Decreasing your tire pressure will also help provide traction -- check your tire specs or ask a bike shop for advice on your specific tires.
Cornering in the rain is particularly challenging. The League of American Bicyclists suggests taking turns slowly and deliberately, shifting your body weight to the bottom of the outside pedal. Braking should be avoided, but if necessary, brake slowly and allow even more extra stopping distance.
Be extra cautious when the rain first starts to fall -- even if it seems like it won't last long, it's already started to create hazardous conditions. The first few minutes of rain riding are often the worst, because oil that accumulates on the road (from cars and trucks, spills, and runoff) rises to the surface and forms a slick coat that's very difficult to see. Crossings, sidewalks and metal fixtures (such as bridges, grates and rail tracks) will be especially slippery.
Your bike, of course, is another key part of the equation. On the next page, we'll discuss how to ensure that you've adequately prepared your bike for bad weather riding.