In that same bathroom mirror scenario, if you move yourself to a 45 degree angle and again photograph the mirror, you'll no longer see yourself in the reflection. It's likely to be the shower curtain or the bathroom wall or whatever is on the other side of the room reflected in the mirror at that angle. It makes sense, right? Shiny surfaces reflect, so what you see in the reflection is what you're really photographing.
For my money, that's the fundamental principle you need to understand when it comes to lighting reflective objects. In technical terms, it's summed up like this: the angle of incidence equals the angle of reflection. But here's what that means in practice. Learning to light shiny objects involves seeing what the subject "sees" in its reflection. Only then do you know where to position your camera and your lights.
Back to the bathroom mirror. What if you needed to light it for, say, a catalog shot? I would position my camera and a white card such that the fill card's reflection—blank whiteness—covers the entire surface of the mirror. Then I would light that fill card with a broad soft light at the most basic level, or by creating a gradation from light to dark across the card, which would add a bit of dimension to the reflection in the mirror. The latter is a straightforward but powerful way to more artfully shape reflections. And the results are terrific.
What if that reflective surface isn't truly a mirror? What if it's simply the shiny glass of a wine bottle, or the silver finish of a dinner setting? Easy: you treat all of those shiny objects as if they are mirrors too. Remember, when it comes to shiny objects, you always light what the shiny object sees. You build something out of light to be reflected onto the surface of your subject. Typically that's a white fill card, a softbox or a piece of diffusion material. Soft, diffused light looks exceptional when reflected in shiny surfaces.
This doesn't seem so difficult, right? It gets harder when the reflective surface you're photographing is not perfectly flat. The spoon in a silver place setting, for instance, is essentially a concave mirror that bends reflections and makes them more difficult to control. Worse is when you're faced with a shiny subject that has a convex shape—a round glass Christmas ornament, for instance, or the crystal of a wristwatch. These surfaces are not only highly reflective, but because of their shape they see omnidirectionally. Now you might be faced with a reflective surface that kicks back to the camera a 180-degree view of the room in which you're working—photographer and camera included. So how do you successfully light a round, shiny object? By lighting what it sees, and starting by limiting what it sees—because it naturally sees a lot.
When faced with round reflective objects like watches or wine bottles, it's not just the highlights you have to worry about but the shadows as well. Use soft white light where you want highlights (from fill cards or silks) and use negative fill where you don't—black cards or flags. In practice, when working with round shiny objects, the larger your reflector the better. Because small cards won't cover the broad area that's reflected in the surface of the object. But a large card placed close to the subject, offers complete coverage with highlights and shadows.
You'll also want to hide yourself and your equipment in shadow whenever possible. That means controlling spill to keep yourself and your camera in the dark, and working with a black tripod instead of a silver one, while wearing dark clothes instead of light. These simple things can make a big difference in the finished shot.
I stock my studio tabletop kit with a variety of white and black fill cards from 4x4 feet down to 8x10 inches and even smaller. But it's the big cards—made of white and black foamcore—that see the most use. I can essentially build a box in which to photograph a round reflective surface, selecting white sides and black sides where appropriate, and ensuring that the reflection on the surface is uniformly maintained to the horizon line. I prefer this approach to a "light tent" because I find it easier to control highlight and shadow when I can easily adjust the distance from reflector to subject, and switch from white fill to black negative fill in the blink of an eye.
What if you're working with a very large shiny object, like a car? You'll notice that in big studios, car photographers work with large softboxes that may be 30-feet long or more. If you don't have a studio at your disposal, you can accomplish the same thing by photographing a car under a diffuse sky. Most often this is done in the desert after sunset. The desert landscape is minimal, so the reflections in fenders and quarter panels will be minimal as well. (Remember, it's all about what the surface "sees" in its reflection.) And the indirect illumination from a twilight sky will act like the largest glowing softbox on the planet.
Ultimately, the simplest rule of thumb when it comes to photographing shiny surfaces is to use soft light. In the outdoors that's a diffused overcast or twilight sky. In the studio, it's a big softbox—which is made proportionally larger by positioning it close to the subject—placed so its reflection can be seen through the viewfinder and adjusted accordingly. As long as you're working with diffused light to control what a shiny surface "sees" in its reflection, you'll have no trouble lighting mirror-like subjects.