There are two reasons to clean your DVD player: to perform general maintenance and to wipe up spills. For general, light cleaning, just dust the DVD player case once a week or so with a damp cloth, and try not to spill maple syrup directly into the vents. If you do somehow actually spill something wet or sticky onto the outer casing, unplug the player immediately and wipe down the surface with a soft cloth and a gentle cleanser. Make sure not to spray the surface of the DVD player directly, as any drips or seepage from the cleaning fluid can cause serious internal problems.
If you're having a serious problem with your DVD player, nine times out of 10 it's because the lens is dusty. This can be a pain because, as you may have noticed, the lens is located deep inside the DVD player and you probably won't be able to reach it without busting out an adorably tiny screwdriver. Instead, you'll have to rely on cleaning discs -- yes, the very same discs forbidden by DVD manuals! Cleaning discs are designed like regular DVDs, but with a tiny brush on one side. As the DVD spins, the brush knocks off dirt and dust particles from the lens. It's great when it works, but use with caution. The brush is really just moving around dust, which means it can also knock more dirt onto the lens or just move dust around inside the machine for it to settle later.
Unless you're watching DVDs in a lumber mill or a mummy's tomb, dust isn't going to be a problem for you. What will eventually prevent your DVD player from performing its best is dust accumulation around the vents. All you have to remember for cleaning the vents is to avoid blowing dust directly into the DVD player. For that, a vacuum cleaner or an electrostatic or microfiber duster work great. Just be sure that you always dust away from the vents and toward the floor to keep from spreading more dust into the air.