Put on gloves
Remove any solid vomit with paper towels or a plastic scraper
Blot up as much liquid as possible with clean paper towels or a cloth
Mix cold water with a small amount of mild dish soap
Blot the stained area with the solution
Avoid rubbing the carpet
Blot with clean water to rinse
Blot dry with towels
Sprinkle baking soda over the area
Let it sit until dry
Vacuum the baking soda
Repeat if needed
Use an enzyme cleaner if odor remains
Allow the carpet to air dry completely