The presence, and absence of beggars in India is something that is worthy of note. To be honest, I had expected much more of them, and we probably have much more in store than this, but our first encounter happened outside Landmark on the first day we arrived. As we walked to the auto a woman and her child came over and trapped us as we sat in the auto waiting for the driver to start and pull away. They both stood there, knowing that we were held captive for a few uncomfortable minutes, fingers of the right hand pinched together and moving up and down to the mouth in an eating motion.
This wasn't the worst, but it was still uncomfortable. Compassion is no stranger to me, but neither is reason, and the act of handing money to a beggar of any sort achieves nothing in the grand scale of things. It confirms their concept of westerners as being good targets, thereby making other tourists' stays less comfortable, and does not do anything to alleviate the poverty, disease and ignorance that allow this situation to arrive. Now everyone must make the choice that suits them when it comes to beggars, and having been there I can tell you it is a difficult choice - try saying no to a girl whose face is scarred with leprosy after walking out of a shop in which you have just spent enough to feed her for several months!
But these beggars, many scarred or maimed in some way, or simply old, are often professionals, and controlled within a hierarchical "beggar's guild" to whom they must pay a percentage of their "donations". Stories abound of children deliberately maimed by parents in order to increase their earning potential, or passed from one beggar to another to add that child leverage on the guilt factor.
It is not an easy choice, but the futility of such short-term gestures is overwhelming to me - you achieve nothing positive other than assuaging the ego for a short while from the raging guilt that says that things like this shouldn't happen in "modern civilisation". Better, in my opinion, to donate your money to an established charity that focuses on education and medium/long-term projects to improve the lifes and remove the root causes of poverty. My opinion.
So, I guess you want some tips for dealing with these beggars. I have had some success, and found the trick is to completely ignore them. And I mean no completely - no acknowledging them, no trying to get away, just keep doing what you are doing as if they are there - no interaction whatsoever. It can be very difficult, but this is the way that most Indians act in the presence of everyone else anyway, so practice the "Quantum Perception" (apparently I didn't invent this concept ;-) that Indians have mastered in everyday situations before "going live" with beggars.
If that becomes impossible, a strong "waving away" gesture and saying, "No!" in their local language may do the trick. The secret is to be confident in this dismissal, something which I seem to have mastered by the number of times they turn and walk away from me. If you hesitate for one second they will keep at it again and again. Even so, do not expect them to leave, or to stop pestering you. Do not expect anything except all that India throws in your path, some of which is not so nice. And keep walking.