A first date is always stressful. You want to make the right initial impression, but you also just want to relax and be yourself. If you really like this new guy, and want to know how to get him to call you after the first date, then plan your strategy well. Go into the date like a military campaign: plot your every move, including an exit strategy.
Your first consideration should be your wardrobe. There is a fine line between flirtatious, and trampy. You'll want to show a little skin, but not too much. For example, if you're planning to wear a short skirt, don't show any cleavage, and vice versa. Never give him the impression that you will take your date to any other level beyond friendship. Surround yourself with an air of mystery. This will keep him coming back for more.
The next step to take in your quest to get him to call you after the first date starts the minute you answer the door. If he brings you flowers, accept them coyly. Don't show him that you are jumping up and down inside. Keep your conversation light. Don't tell him your life story, including the one about your favorite cat's untimely death. This will scare him off, and leave you sitting home next Saturday night with a pint of ice cream.
When you reach your destination, whether it be a restaurant or a movie theater, have fun, and be flirtatious, but not too clingy. Nothing pushes a man away faster than a needy woman. Don't ever play stupid. Contrary to what your mother might have told you, men do not like dumb women. Let him see how intelligent you really are. If he can't handle it, let him walk away. Ask him a lot of questions about his favorite subject: himself. Men love nothing more than keeping the conversation about their hobbies, likes and dislikes. When the date is over, let him make a move. If he doesn't, just say thank you, and head towards the door.
If you really want to know how to get him to call you after the first date, then don't wait for him to do it at all. Get his number and call him yourself. You are, after all, an independent, modern woman. Just don't be obnoxious and ring him every fifteen minutes. Call him once, and only once. If he is really interested, that is all it will take.