OK so I get that the miners are somehow involved in confirming payments. Am I right to assume that a payment will remain unconfirmed until the next block is released?
That all depends on the recipient.
SatoshiDICE for instance, can accept payment on 0/unconfirmed because they turn around and use those funds in the payout. So if the wager never confirms, the payout will never confirm either.
A retail merchant, for instance, might not really be worried that you'll try to double spend on that 2 BTC purchase, and might have no problem accepting on 0/unconfirmed. (There are configurations a merchant would follow to protect against a race attack).
Most exchanges and merchants require six confirmations as that is the level where the chance of reversal is mathematically not ever going to occur.
Once that block is released, will you always have only 1 confirmation, or is it possible that more than one miner has confirmed your payment in between the time you made it and the time before the block gets released?
This is a good article describing the process:
It includes the following infographic:
(Those boxes in the top-right are an illustration of the block chain.)
So if your transaction is first included in block 1,000 then it has 1 confirmation. When there eventually is block 1,002 it has 3 confirmations. At block 1,005 it will finally have the 6 confirmations that most exchanges and merchants require.
Can you get more than one confirmation in each subsequent block? In other words when people talk about the magical "6 confirmations" will that always take almost an hour, or is it usually done faster?
Bitcoin mining's algorithm targets one block every 10 minutes. In reality, variance plus changes in hashing capacity will cause that "six confirmations" to occur as quickly as a fraction of an hour or as long as several hours.
Also, who gets the miner fees? I understand that the fee is an incentive for a miner to confirm your transaction. Does the fee go to the first miner to confirm or is it shared among all the different miners that confirm once you have several confirmations?
While there are cases where a block at a certain height is solved by a second (or third) miner, all but one of those blocks are eventually orphaned, and thus the coins in their block reward will never confirm.
You can see this visually occur here:
So if you are solo mining, you get the block reward as well as the fees. if you are pool mining, what you get is whatever the pool you participate in offers. Some keep the fees. The fees currently are a tiny fraction of the amount of the block reward though. Every bit of helps though I know.
What is the size of a typical fee and does it really help to get your transfers confirmed faster, or is that propaganda to get us to "support the network?"
There's a huge difference between no fee and at least the minimum fee. Without a fee, your payment might not get included in the next block based on a few factors (age of the coins selected for the transaction, amount of the payment, etc.). If you include the fee recommended by the client, the payment will likely be included in the next block or two. If you add a much higher fee, it still will likely be included in the next block or two. (i.e., paying above the minimum doesn't really help get it to confirm any faster.) The goal is to get it included in a block. After it is in a block, it continues to gain confirmations with each new block, regardless fo whether or not it had a fee, or the amount of the fee.