Assuming you are referring to the pedigree/race record, simply roll back the upper lip and take a photo (using a 4MP or higher) of the horses upper lip, with a towel around his eyes, so, as not to frighten the horse. Download the photo onto your computer (if you don't have a computer, try the local library) and print out the photo of the horses inside upper lip and retrieve the number that is tattooed on the inside of the upper lip. Get in touch, using the yellow pages, with your local equine veterinarian and explain to him what you want...or you could telephone the nearest standardbred/thoroughbred racetrack and speak to the racing secretary's office.
If a horse does not have a number tattooed on the inside of his upper lip, he never raced. Before every race, and before the horse is even allowed onto a racetrack, the upper lip is rolled back and checked against existing records of identification to make certain the right horse as listed in the program for the fans to wager upon is the correct horse.
You could by-pass the entire procedure if you are able to obtain the tattooed number from the horses inside upper lip, but, unfortunately, the tattooed number becomes worn with age and is difficult to see with the naked eye.
Or, you could simply ask the previous owner and take it for what its worth. But, at least the previous owner might narrow down the state in which the horse raced, then you would be able to get in touch with the racetrack secretary's office of that racetrack in that state.