Partially painting your computer's monitor can be a very effective aesthetic enhancement, particularly on an old monitor whose casing has begun to turn yellow. A good colour selection can even enhance your viewing experience - my charcoal monitor offsets graphics much better than ugly off-yellow plastic. Painting just the front is nowhere near as risky as painting the entire monitor, as the heat produced near the front of the monitor is virtually null, and the air holes are guaranteed to remain untouched. It also takes a lot less paint and effort. The following assumes you're using 3/4" and 1/8" brushes, as this is the only method I've tried.

The front panel of your monitor is probably plastic, so oil based paint is the best choice; it's less likely to get scraped off due to general wear and tear. Conversely, water based paint is easier to use - it has slightly friendlier fumes and is far easier to clean up, but you'll have to be much more careful with the finished product. Water based paint may last longer if a coat of primer is used underneath. A high quality paintbrush is less likely to shed hairs on the paintwork and will probably withstand contact with oil paint better. If you can be bothered removing loose hairs yourself, or you're just not picky, just about any brush will do.

It's generally advisable to put masking tape over any part of the monitor you don't wish to paint. Note that paint can seep underneath masking tape - the tape's purpose is mainly to avoid direct application of paint. This doesn't absolve you from responsibility, but it will probably make your job marginally easier. When painting the area directly adjacent to your screen, be particularly careful, tape or no tape; excess paint could seep between the screen and the monitor case. I chose to use a fine brush for this part, and kept a damp cloth nearby to remove any misplaced paint from the screen immediately (having foregone masking tape through laziness).

For best results, it's advisable to use at least 2 coats of paint, waiting for it to dry between coats. Streaks and other errata are more easily visible when the paint is dry; also paint is marginally darker when wet and this makes it harder to see if any evil beige is showing through. If you can't be bothered repainting your monitor at this stage, at least consider touching it up; you'll probably spend a lot of time looking at it!