1. Search out an experienced positive reinforcement trainer or behaviorist to help you evaluate potential adult dog candidates.
Make sure they have experience with assessments of adult dogs (18 mos plus) and what the results of the assessments indicate and if or not they would recommend a specific dog. Ideally, they will also have experience assessing potential assistance dogs.

Remember that you want to evaluate dogs that are have ideally been in a home environment for at least a month, not a shelter as their behavior may be quite different.
Try to find a CARAT evaluator. If they are not available then ask around so see who might be available locally. Get references from other people whose dogs they have assessed and ideally. What you want is someone who will tell you he truth about the potential of a specific dog to become an assistance dog and what pitfalls they see in the dog's current temperament and what behaviors can potentially be a problem for you to change. This person will need a detailed list of what your tasks are and the types of environments the dog will be working in.

2. Review the characteristics of a service dog and also the characteristics to rule one out. Start your search by calling local breeders, rescues, service dog training programs etc to talk to them to see what the potential is for a dog that can meet your needs to come in. If you do the preliminary footwork yourself in the search, you will save your self much money and also get to know the reputation of the people and organizations you are dealing with. 
Visit the potential dogs first so see if they might meet your needs. Get as much information about the dog's background as you can. Vet reports, foster home findings, any known history about who the dog lived with etc. 
When you find a dog that looks like it might be a candidate, then bring in your evaluator for a more detailed look.  If you can be present for the evaluation, that is ideal. Stay out of the way unless they ask for your assistance.  Set aside time to discuss the evaluation with them. 

3. If the dog is currently with the original owner, have them fill out the "Dog Assessment Test" as honestly as possible. 
I've called it the "Dog Assessment Test" to defer them from the focus of the test-assessing impulsivity of the dog. 
They rate the dog on a scale of 1 to 5 for each question. If they don't know the answer, there is a box for that as well.
Impulse Control Test PDF Check-list ]

After they have filled out the form, scoring is as follows: (taken from the study).

"Scores for all of the questions that had been answered were summed, and the total was divided by five times the number of questions which received scores (since five is the maximum possible score for each item). So for example, if all 18 items were scored, the sum of the scores was divided by 95 (18x5). This gave a final score within the range 0-1 that described the rating of the dog’s level of ‘impulsivity’ (where impulsivity is defined according to the reliable items extracted from the expert survey); high scores relate to high impulsivity, or reduced self-control. This was termed the “Overall Questionnaire Score” (OQS)."  
A low OQS is desirable for a potential service dog candidate.