About the Skill:
Begging is the skill by which one may acquire gold and items from NPC's simply by asking. Since the items seldom amount to much value (even at GM skill level) Begging is typically considered a Useless Skill (though some special items have been made available during Halloween events). Most players who undertake it do so solely for roleplaying.
Note that the use of Begging lowers karma by a small amount.
Successfully begged NPCs will give gold dependent on your karma level. Note that it is possible, by bringing your karma low enough, to receive a negative amount of gold. These bugged stacks will be labeled as "A Gold Coin" and, when you attempt to move them, will display a total of around 65,535 coins in the pile (the amount you were supposed to end up with is the indicated value minus 65,536).
The stacks cannot be divided and are only really worth the same as one coin for the purpose of purchasing items or creating checks.
Elves in Heartwood (and Darius the Wise in Moonglow) provide various items instead. These each have an "Acquired by Begging" tag affixed to them and are unstackable.
There seem to be different levels of rewards. The theory is as follows:
75% Level 1
24% Level 2
1% Level 3
How to train:
You can buy Begging from any gypsy found in Brittania and at any Gypsy_Camp. Activate the skill via macro or skill button and target an NPC. If you do not gain you must find another NPC to target. If you do gain you can target that and every previous NPC again for gains.