Search online or in the phonebook for an indoor rock climbing gym near you. Most major cities and some smaller ones have gyms. When you find a gym, find out about instruction that the gym offers. Most offer free introductory classes to teach you the basics about equipment, climbing etiquette and how to belay and top-rope with a partner. Some gyms provide private lessons to improve your technique.
If you decide climbing is for you (very likely possibility), become a member. Year memberships are expensive (range from $350 to $550, depending on location), but are less expensive than paying each time you climb. The money that you spend might be an additional incentive to keep you climbing!
Gyms will offer some necessary climbing gear for rental, but if you plan to climb often you'll want to get your own.
SHOES Prices for climbing shoes starts at around $50. It's best to buy them tight (at least a half size smaller than your street shoe). They should be uncomfortable, but not so tight that your toes curl up and can't move. Shoes are available at most climbing gyms, and staffs are generally knowledgeable about the different types of shoes.
HARNESS Harnesses also range in price starting at $50. Make sure to try-on the harness before you buy it (you will hang from a wall in it, make sure it's comfortable!).
CHALK BAG Climbers use chalk on their hands to prevent sweating, which makes the rocks slippery. Climbers most interested in top-roping will often get smaller chalk bags (usually around $20) that they can wear around their waist so they can use the chalk during a long climb. Climbers that boulder more often will get larger chalk bags (around $30) that they keep on the ground and use between tries.
FRIENDS You'll need someone to belay for you when you're top-roping, so bring a friend (don't worry, if you don't bring one you'll definitely make a few!).
BELAY DEVICE The belay device is what lets you support other climbers and help them get up the wall safely. When you set the belay, you pull up the slack of the climber. If he or she starts to slip or fall, you pull the rope taut.
CARIBINERS These are the clips that connect you to the rope, mountain and numerous other climbing devices (they make good water bottle clips, too!).
After you climb in the gym, you should try climbing outside (most climbers say that climbing outdoors is what hooked them). Talk to climbers at the gym and ask them when their next trip is.