Please note my answer is entirely based on my own experience, and based on South Asia (which I know a lot and currently live), and South East Asia (pretty much same, but relatively developed).
The very first thing is that the beggars are not necessarily poor people. In Asian countries, begging is more of an underground business that works as a network. The only difference is it's highly unlikely that they will threat you.
- Beggars work as a network. In most cases, there is a leader (not necessarily a beggar himself).
- Getting into the "network" is difficult no matter you are cheating (no real reason to beg) or not.
- Beggars get physically harmed if entered the "zone" without the leader's acknowledgement.
- Some carry a baby, an old women, claim they are blind or deaf, have physical disabilities, etc. Believe me some beggars commit them themselves.
But beware, there are some beggars addicted to drugs. They don't care if they get food or not, a place to sleep or not, but they must find some money to buy drugs. Don't be surprised if they carry a hidden knife or something.
What is the best way to "get rid" of a beggar without being outright
disrespectful to them?
Depends on the beggar. I don't really want to sound like a jerk to say you to not help anyone. Help someone if you really feel like.
Male, middle aged and seems like a drug guy - Don't look in the eye and show you are surrendered or lost. Even if it's obvious that you are a tourist, just show them that you know what you are doing and where are you going.
You will notice they beg you in particularly if you are the only tourist in the group. Just observe how others behave and act so.
It's considered rude if you blame them or get mad at them.. In a country with mixed religions, this will be tolerated but if you are a guest to the country, religion and sometimes the race, locals will find you not friendly and will be passive aggressive.
Don't be a lord either. One buck of your currency will be a lot for them, but don't try be a huge contributor. This raises a lot of awareness and your next taxi driver, taxi driver and others will tend to charge you more.
I have a my own rule of thumb. If the beggar seems to be a legit one and really needs any help, I give him money equivalent to a price of a daily newspaper of their local currency. I don't know if this works everywhere but tried this on 4-5 Asian countries - it worked.
Better yet, buy him a lunch. Everyone will appreciate you. (Make sure it's a general lunch and not fancy type or something the locals don't eat :) )