Put on gloves and remove any solid vomit with paper towels or a plastic scraper
Blot up as much liquid as possible with clean paper towels or a white cloth
Mix a small amount of mild dish soap with warm water
Dampen a clean cloth with the solution and blot the stained area
Repeat blotting with fresh cloths until the stain lifts
Rinse the area by blotting with a cloth dampened with clean water
Blot dry with towels to remove excess moisture
Sprinkle baking soda over the area and let it sit until dry
Vacuum up the baking soda
If odor remains, apply a pet-safe enzyme cleaner according to the label
Let the carpet dry completely
Repeat the process if needed