Trace over the marker with a dry-erase marker if the poster is glossy. The dry-erase ink will bond with some or all of the marker ink on the poster. Don't draw on non-glossy posters as it won't come off those surfaces.
Wipe the dry-erase ink off with a paper towel or cloth. The dry-erase ink will immediately come off and will take some or all of the original marker with it.
Repeat the process until all the marker is gone or until it is as light as possible.
Dampen a cotton swab with a solution of 1 tablespoon spirit of salts and 4 tablespoons water (if the stain is still visible). Squeeze the cotton tip end so it is as dry as possible. This will prevent you from soaking the poster.
Place a few paper towels on the back of the poster, opposite the marker stain. This will help absorb any liquid and keep the poster from getting soggy.
Blot the spirit of salts solution on the poster.
Repeat the process until the marker stain is gone.
Keep the poster flat on the working surface for several hours until it is dry. Don't hang it up before it is dry as this could encourage tearing.