Answer:
You need to join a club for that dog breed, and to show him. Showing a dog is the only and best way breeders will be looking for future stud dogs. This can only be done if your dog is purebred with a great pedigree. The dog also needs to be health tested, usually eyes, hips and elbows. The type of health tests depend on what breed the dog is. Please note that health tests are NOT the same as health checks, where the vet just looks the dog over. Tests require several hundred pounds/dollars.
Also, a stud service is not just sticking two dogs together and hoping for the best. You need to be prepared to get very intimate with your dog (sometimes they will need help), and to calm a dog down if either female or male become aggressive or fearful. Mating two dogs, if done incorrectly and without firm handling, can lead to both dogs injuring themselves. It may be best to find a mentor at first, to limit these risks.
If your dog doesn't have papers and not health tested it would be very irrisponsable to use him for stud service.