When dealing with a pet stain, response time is most important. Prompt action will increase the odds of successful removal. There are products out there that, when used on some natural fabrics and/or fibers, can actually set a stain or even worse, "bleach" out the affected area! The fabric/fiber type to be treated should be identified and even tested in order to avoid permanent damage.
Our pet spotting product of choice for treating pet urine, vomit, feces, etc., is Biokleen "Bac-Out". This enzyme product will break down the stain and/or odor by digesting it. Although it doesn't get every pet stain out (especially if they are old or on a natural fiber/fabric) if you get to the source, you will have a more legitimate chance. Bac-out is safe to use on many different fabrics/fibers and can be used in a variety of numerous ways.
Club soda works pretty good for pet accidents. It is only effective while the soda is effervescing, so you may need to treat an area several times. Start by blotting the area before pouring the club soda on it. Once the soda has stopped fizzing, immediately blot the spot again, repeating as necessary. If the stain isn't fresh, you'll likely need to follow up with a baking soda treatment.