Let's start with the easier stains and work up to the tougher ones.
Glass, Metal, Laminate or Whiteboards
Try tracing over the stain with a dry erase marker. The dry-erase marker contains solvents that help break down the permanent marker ink, making it easier to remove. Wipe the area with a paper towel or microfiber cloth and hope that the stain lifts right off. Repeat the process if necessary.
Dry erase markers tend to work better on fresh stains. So, if that doesn't work, another method is to dampen a cotton ball or soft cloth with rubbing alcohol. Gently dab the permanent marker stain, allowing the liquid to break down the ink. Wipe the area with a clean cloth to remove any remaining residue.
If you don't have rubbing alcohol, you can try nail polish remover — but test it out first, as acetone can damage certain surfaces.
Plastic or Wood
Rubbing alcohol is also a good choice for plastic or finished wood.
The dry erase marker method might work on some plastics, but avoid it for wood, as the surface can absorb both the permanent market and the dry-erase marker, making these stains even harder to remove.
Avoid acetone, as it might degrade certain plastics or wood varnish.
Tougher Stains
For tougher stains on hard surfaces, sprinkle a bit of baking soda onto a damp cloth. Gently scrub the stain in circular motions until it starts to fade. Wipe away the baking soda residue with a dry cloth.
You can also try toothpaste and baking soda.
A Magic Eraser (melamine foam sponge that is a cross between a sponge and sandpaper) might also do the trick. Dampen the eraser slightly and gently rub the area without applying too much pressure. Wipe the surface with a soft cloth to remove any remaining marks.