The mating process between a stud and dam (with the aim of breeding) is known as a stud service. The owner(s) of the stud will act as an advocate for their sire (by using advertisements, networking at performance events, etc), allowing dam owners to come forward and express an interest in the stud.
Both parties will have expectations about what they wish to gain from the experience. The owner of the dam will usually be concerned with the health, aesthetics, and genes of a stud with the aim of producing puppies with desired qualities. The stud owner will also be concerned with selecting the most complementary dam for his stud. In exchange for services, the stud owner will receive a stud fee and will usually be guaranteed the first pick of the litter if breeding is successful.
The service also extends beyond just purely allowing a dam to mate with a stud. If you are a stud owner, you will be involved in the inner workings of the process from beginning to end. For example, you will be expected to guarantee a certain number of puppies, assist the dogs in the mating process (if required) and care for the female throughout.