One way to go about this is to work with local dog clubs for your breed.
Here is the website for a Cairn dog club in your state
http://www.chi-cairn.org/
You might also find this site useful
http://www.doggies.com/Cairn_Terrier/Illinois
And in some cases running an ad in the local pet column or asking at your vet might find you a contact with a stud.
You may be asked to make sure your dog is free of brucellosis or tested for health issues before a stud owner would agree to a breeding.
Hope this helps you!
Dog Expert:Rescue, Train,Breed,Care
30+ yrs dog home vet care & nursing, rescue, behavior&training, responsible show breeding, genetics