Foot Fitness: Climbing, for the beginner, imposes a lot of new physical demands, not only on the hands but also on the feet. The distribution of your body weight over your feet while climbing is similar to standing on the tips of your toes for long periods. The big toe must support your whole body weight and the calf muscles are stressed trying to keep the foot horizontal. Beginners will often complain of shaky legs. This is either a result of unfit calf muscles or it may be a result of excessive muscle tension as a result of being a little nervous. The best way to gain the specific fitness required (and learning to relax in exciting situations) is to climb regularly. 
Footwear: To climb well it is essential to develop good footwork right from the very start. But it is only really possible if you have a well-fitting pair of climbing shoes. When buying your first pair of climbing shoes, fit is the most important consideration. They should be comfortable when they're tight. You shouldn't be in total agony! 
Footwork:
Placement :Good foot work is fundamental to good technique. If you use your feet well, a greater range of techniques will become available to you, you will take more weight off your hands and your precious finger and you will preserve arm strength. Words such as precise and purposeful are often used to describe the footwork of good climbers. This should be your goal. Even when standing on large foot holds choose the best part of the hold to stand on, use the toe of your shoe and don't take your eye off your foot until it has been placed accurately on the foot hold. By placing your feet accurately, even on the largest holds, you will get in the habit of looking and placing your feet carefully. This way, when you start climbing the harder routes that generally have smaller foot holds, it will already be second nature. 
Use your toes: It's important to use the toe of your shoe when placing your foot on the holds and at first this is usually the inside edge of your big toe. The advantages of using the toe of your shoe on any foot hold are that you can stand on smaller holds, you don't loose any height (if you place the arch of your foot on the hold you instantly loose 10 cm), and you can spin on the foot hold, which is important in many of the more complicated movement techniques. 
Remember: Choose the best and/or most appropriate part of the foot hold to stand on. Place your foot purposefully, using the tip of your toe (usually the very front inside edge of your shoe) and place it once only (don't jiggle it around). 
It is also critical to learn to trust your feet. 
Change the direction of your feet ?Backstepping 
Once you have taught yourself to be precise and purposeful with your feet the next step is to experiment with the direction your feet are facing. 
If you watch beginners they very rarely backstep which is using the outside edge of a shoe against the wall, they usually climb with both feet facing outwards. It is important to realise you can change the direction your feet. There are many situations where backstepping is an advantage - for example, when you are laying away from a hold back stepping is usually an advantage and on slabs where the emphasis is on your feet your foot direction will be changing constantly. 
Basic Foot skills - Crossing through and swapping feet
As you can see, we are gradually expanding our foot movement skills. Once you are placing your feet precisely and you realise you should be changing the direction of your feet where appropriate, it is time to move your feet around. The two most important foot movements that make it possible to link the more complex movement skills together are crossing your feet through and matching or swapping feet.