Start slowly. The first step should be a simple hello or an introduction. Starting too quickly and aggressively will probably make him see you as someone to avoid. Shy guys want to avoid embarrassment, and they won't want to be around someone who is loudly calling attention to them.
Get to know him. A shy guy may not be as shy once he gets to know you. If you let him get to know you, he will probably open up about himself. This will allow you to spend more time talking with him.
Be subtle. Now that you are spending more time together, you can slowly flirt your way to a date or two. Use mutual interests as an excuse to go places together, working your way up to dinner and romantic occasions.
Touch and compliment him. Once he's comfortable going places with you and talking openly, you need to leave little doubt about your real intentions with him. Touching him on the forearm or shoulder, taking his hand and touching his cheek will let him know that without being too aggressive. Further drive the message home with regular compliments. Compliment his looks, physical abilities and anything else that you find impressive. Pretty soon, your shy guy will flirt back with compliments of his own.