Two things work, depending on what sort of marker it is:
If it's "dry-erase," use Murphy's Oil Soap. Yes, the yellow stuff that cleans floors. Wet the stain with water, dip a very soft, old toothbrush in full-strength Murphy's oil soap, and gently gently rub, keeping an old towel (preferably white) beneath your stained item. If the ink starts to lighten, even a little, it will probably come out completely with time and patience. Rinse, repeat, rinse, repeat. Over and over. Be warned, there is ALWAYS the chance that you'll tear through the silk before you get out the ink. But I've had excellent results (and a few not so great ones) with Murphy's Oil Soap. Oldest child came home from school with dry-erase marker on her dresses on a weekly basis.
If it's "Sharpie/permanent marker" pure acetone will remove it, as Melanie suggested (although it may or may not destroy the item in the process). Get it at a drug or beauty supply store (not the same as regular nail polish remover, which won't work). Don't know if I'd try this on silk. Works like a charm on cottons, linens, wool. I know because my toddler took a Sharpie to my entire office, including a custom-made slip-cover on my club chair. All Sharpies were removed from the house for the next 3 years!