At the tailor, you are looking for pictures, example pieces, alteration miracles – you are looking for samples of their work that validates the tailor's claims of greatness.
If the overall garment looks good, spend a few minutes studying the details – does the stitching look secure and clean, is the build and silhouette something you want in your clothing.
Do not choose a tailor who doesn't have anything to show or happy customer to refer you to.
Your tailor is a very very personal helper. He needs to know what kinds of style you like, what he feels will make you look better, and how to mix these two requirements together.
You have to feel comfortable telling him what kinds of styles caught you eye on the magazines, and to trust his recommendations.
If your tailor is too busy, try going at a less popular time, even if you have to apply for leave from work. It will be worth it when you put on the shirt of your own design.
Communication is vital, and making certain that both sides clearly understand and respect each other is key to a long term partnership.
Finally, what is your gut feel about the tailor? After talking to him, looking at his workmanship and seeing his shop, do you feel that this is someone you can have a long term working relationship with??