I am unsure how I go about advertising my dog for stud?

Generally you don't need to ..if your dog is shown and does really well you will have owners of bitches knocking at your door ;)

Some breeds advertise their studs in their breed club magazines, along with their pedigree, health results and show or working wins. So you could try that, the cost is not a lot and you will be in direct contact with the people most likly to be interested. What breed?