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You want basic white toothpaste. Not gel, whitening paste, or anything with abrasive crystals in it. The traditional white paste will do the trick without damaging the wood. Sometimes rubbing alcohol or peanut butter can be used in place of toothpaste to remove marker stains, but toothpaste is usually more effective. You want to make sure the spot you're removing is accessible and flat, so that the toothpaste doesn't run down the surface while you're trying to rub it in. Make sure your marker stain is covered with a thick layer of toothpaste. You can apply more later if you don't have enough. Grab a clean washcloth and hold it under running water. Any temperature that's comfortable to you is fine. Once the washcloth is soaked, squeeze any excess water so that it's damp and not dripping wet. Using a circular motion, rub the toothpaste into the marker spot for three to five minutes or until most of the toothpaste disappears. Apply enough pressure that your toothpaste can penetrate the marker, but not so much pressure that you're going to damage the finish on your wood. Add more toothpaste if the washcloth doesn't move freely over the entire surface of the marker stain. Using your damp washcloth, wipe off any toothpaste that's still left on the wood. Make sure you wipe in the direction of the wood grain, not against it. The wood will dry and any toothpaste should be gone. Your marker stain should be removed. All you have to do now is clean up your area. Put away your toothpaste, dispose of your washcloth to be cleaned, and replace your wooden object if it's movable. Repeat the previous steps, but add an equal amount of baking soda (for the amount of toothpaste) to your stain. This will add abrasion so use caution when you're rubbing the mixture into the wood. If the baking soda doesn't work, follow the same steps using rubbing alcohol or peanut butter. Be sure to wipe away the alcohol or peanut butter with a damp washcloth, then let the wood dry before cleaning up.
Get a tube of regular toothpaste. Turn the piece of wood so that the stain is facing up. Squeeze a generous amount of toothpaste onto the surface of the wood. Dampen a washcloth. Rub the toothpaste in. Wipe away any remaining toothpaste. Clean up your work area. Add baking soda if any marker stain remains.