Gauge the interest of your date. Obviously, if she has been giving you the cold shoulder all night long, then she does not want to hold your hand. Look for signs that she'd like to initiate contact: gentle and playful shoving, brushing her fingertips accidentally against yours as you walk or holding onto your arm. These actions mean that she is waiting for you to make the move.
Wait for the right moment. Trying to hold hands over dinner could become awkward. Wait until the hands are free. The right moment is when you both have your hands free, and are side by side, sitting in seats at the movie, walking after dinner or listening to a concert. Don't wait for a perfectly romantic moment; just wait for the right opportunity.
Put your hands in your pockets if your hands are sweaty. A sweaty first hand hold can hurt your chances for a smooth hand holding experience, so place them in your coat pocket and inconspicuously wipe them off on the fabric. This way, even if you're nervous, your date will never know.
Create the perfect moment to smoothly move into a hand hold by joking that you want to see the size of her hand verses yours. Have her put her hand against yours, palm to palm, and then intertwine your fingers. It's an easy motion from there to actual hand holding. You might also offer a palm reading or ask to see her manicure, as other sneaky ways to naturally move into the hand hold.
Avoid forcing the issue. If you go in to initiate the hand hold, and she pulls away, then maybe she just isn't ready to take it to that level of physical contact just yet. Don't try again until another date and time.