In my bitcoin client there is a transaction fee recommendation of 0.01. Does this mean anytime I send money to someone it'll charge them 0.01 back to me, or how does this work? I read the wiki but confused on who it affects. Who gets the 0.01 and at what point?
This means that every time you make a transaction you give 0.01 to the person who finds the next block. The purpose of this is to encourage people to run miners, because it costs money (electricity). Once it gets to the stage where miners will be rewarded very small amounts of coins for finding a block, the transaction fees will be their main reward. Currently though if you attach the fee you may be sure that your transfer will be added to the next block before the transactions that weren't paid for. If you don't pay the fee it doesn't mean your transaction will not be added to the block, but it may not be the next one created.