There are probably many people in your list of friends and family members that may have used dog photographers in the past, or have an idea of where to look from a recommendation they may have heard somewhere. Word of mouth is usually the most reliable way to go about things because of the fact that people have firsthand experience of what to expect. Check out a couple of dog photographers that other people that you know have used recently to get a good idea of their work.
Budget, like in all cases, is probably the most important aspect of your hunt to find a dog photographer. In your search, you will find many people that cater to the elite class with very expensive packages and those that will give the same quality of work for those with a limited amount of money. So make sure you set a reasonable amount of money aside for your dog photography and keep that in mind whenever negotiating.
Every dog photographer that you visit will definitely have a portfolio. It is natural instinct of every type of photographer because of the fact that there work is only portrayed through pictures and nothing else. Some may have it online while others prefer clients to come in and view the folders of their most cherished pictures. This will give you a good idea of what the photographer is capable of producing.
Consulting with a few shortlisted dog photographers is very important to get a good idea of what your expectations are and what you are looking for when they do actually come over. Discuss money, the number of pictures that will be taken and those that will be developed. Any extra fees that they may have and whether timing is an issue. Everything should be talked about openly.