I would begin by finding a suitable indoor climbing facility. You can find one in most cities, and it will be a good place to start.
Here are some good tips:
Tip 1) Climbing indoors usually means you are following a taped route (using holds for both your hands and feet that only has a specific tape color). Before you leave the ground, think through the route. "If I put my right hand there, is it easier to move my left hand to the next one or will I need to switch?" That way you have envisioned what you will be encountering while you are climbing. Also scope out where your footholds will be as well.
Tip 2) Legs are stronger than arms. Use your hands/arms for balance but use your feet to hold your body weight and propel you up the wall. Think of climbing as a really wierd ladder. You dont do push-ups on a ladder, so dont while rock climbing.
Tip 3) Move your feet before your hands. If you concentrate on moving your feet up to maintain balance, then moving your hands will be easier. On really easy routes, this may feel really boring, but it will provide greater success
Tip 4) Hips in: By pushing your hips into the wall, it will provide greater balance, and transfer more of your weight onto your feet. The more your rear-end sticks out away from the wall the more weight will be on your arms.
Tip 5) Arms straight: It allows any weight that your arms are supporting to be on your hands and shoulders, not your bi/tricepts. Bicepts and tricepts will tire out very quickly if you keep your upper body pulled into the wall. This will also increase the amount of force your hands have to produce to keep you holding on. As a byproduct of keeping your arms straight, you will have greater visibility to the holds above and around you. You can continue to think 2-3 moves ahead so you keep yourself from grabbing a hold with your left hand that would have been better for your right.
Tip 6) If they have climbing shoes, use them: you wouldnt wear football shoes to play basketball, so why where tennis shoes to climb? Climbing shoes are specifically designed for the sport. However you want to wear them very snug (to the point of discomfort, not pain). This will give you more control and better grip as you climb. If you dont have climbing shoes available, then the oldest pair of athletic shoes are best. They will have the least amount of tread on the bottom and the "cushion" will have begin to harden, not providing as much shock absorbsion. This is good because the more cushion in your shoes decreases the amount of force your foot will be able to apply to a hold. Also, tighten them down as far as they go. Less room in the shoe will lessen how much you foot moves around in the shoe.
If you pay attention, you will learn a lot from watching other climbers. Be on the lookout. Also, most climbers are fairly approachable. Some are looking for solitude, but when you meet someone who seems outgoing, ask them for a few pointers.