First and most importantly, you have to decide what type of garden you would like. This includes not only your requirements for the garden but also the style you would like. While there are many excellent designers around, there are also plenty of people who aren't great. I suggest that you ask friends in the neighbourhood or consult your local garden centre or nursery. You'll find advertisements in the back of many garden magazines, but this will not guarantee that the designers will be suited to your needs.
Personal recommendation is always the best.
When you make contact with potential designers, ask them for photographic examples of their work, samples of their drawings and planting plans and a short list of recent and past clients. One way or the other, the process of having your garden designed is an investment and you should not choose lightly. Qualifications from a horticultural college, while useful, are not the only criteria on which to judge someone. Many of the best garden designers are self-taught. Prices will vary according to your requirements, but I would suggest that a fee ranging from 250 to 1,000 would not be uncommon.