The first and main thing you have to do is clean up any food that was thrown up. If you don't do that, you definitely will never get the smell out.
Second, use a carpet cleaner spray like Resolve to lift up the stains. You spray it on the carpet and then you use a clean wet rag to "wipe" the stains away.
After you do that, allow the carpet to dry -- DO NOT VACUUM the carpet -- I speak from experience here -- if you vacuum and you don't get up all of the food pieces, your vacuum will STINK to high heaven... and then every time you vacuum from then on, it will smell like vomit.
Wait until the carpet cleaner has dried and then sprinkle down some carpet freshener and THEN vacuum. You may have to rent a steam cleaner as well to go back over the stains just to make sure that they're all gone.
Fresh air and a fan also help make the smell go away after you've done all of the above.
Good luck! My son had a stomach virus last weekend....