The best way depends on rug fiber, handmade or machinemade, rug value, and how much mess there is. If is valuable, take it to a professional rug cleaner. If not very valuable, read the care label and check with the manufacturer for their advice.

Good advice from apple_pie_order. I've done well with both Oxi-Clean and Folex. You need to mix the Oxi-Clean granules with water. Folex can do an amazing job for certain stains, but I tend to use the Oxi-Clean for anything involving pets.