Im new to bitcoin. Ive read all about how it works but and I think im about 70% of the way to understanding it.
But there are still some burning questions that need answering.
Great, lets see if we can get you closer than 70%.
Oh dear, there's our first problem. The bitcoins aren't printed on the paper. What's printed on the paper are the Bitcoin Addresses that bitcoins can be "sent" to (perhaps it would be better to say "assigned" to), and the "private key" of each of those addresses. The private key that is mathematically associated with the bitcoin address that the coins are "assigned to" is necessary to spend those bitcoins. Without the key it is impossible to spend them. On the other hand, ANYBODY who does have the private key can "spend" them. The "coins" are just a ledger entry in the blockchain. The blockchain is a public ledger that every full peer maintains a copy of. It has every confirmed transaction that has ever occurred in bitcoin. So when you spend bitcoin, your wallet uses your private key as a sort of "password" to allow you to update the blockchain and re-assign some received bitcoin outputs to someone else's address.
Or just grabbed their laptop and copied their bitcoin wallet.
Now there are two copies of each coin in the world.
As you hopefully now understand, what you actually have two copies of is the private key that will be used to create a transaction that will re-assign the value of some bitcoins that are stored in every copy of the blockchain. It's a bit like having two copies of a "password".
Yes. First person to create a valid transaction that uses that private key, will re-assign the bitcoins to a new address where that private key is no longer useful.
does the seller now receive that exact numbered coin 987654 and some kind of transaction is logged or
does the coins number transform when he receives it in his wallet into say 123987654 for example and coin number
987654 is now spent and ceases to exist. ?
Hopefully you're getting a better picture of this in your mind now.
When you received that bitcoin, a transaction was registered in the blockchain. That transaction had an "input" section that carried a digital signature from the private key of person who sent you the coins they received at their address. The transaction has an "output" section that includes a field called "value", and that value was set to 100,000,000 by the wallet that sent you the bitcoin (all values in the blockchain are represented in integers as "Satoshi" values, there are no decimals, so 1 BTC is a value of 100,000,000). The output also has a "script" section that sets up the requirements for spending the transaction you received. In general, those "requirements" consist of a bitcoin address and some instructions on how to compare the address to the signature that will be later provided when it is spent.
When you send that bitcoin, your wallet will create a new transaction. The "input" will include a reference back to the transaction that you previously received. This reference is a unique 256 bit number that exclusively refers to the previous transaction where you received the output. Every peer and every miner will use this reference to go look up the transaction that you received and validate that you have provided the signature and public key that the previous transaction you received required. As such, the input your wallet creates will also include a scriptSig section where your wallet will provide the public key and the necessary signature to meet the requirements that were set up in the output when you received it. The wallet will then create an output to the address owned by the coffee mug vendor. The output will be structured much like the output that you previously received, but with the cost of the mug in the "value" field, and the bitcoin address of the merchant in the "script" section.
of all transactions that have ever happened?.
Every full peer that will participate in validating the transactions and blocks will, yes. It is typically called the "blockchain".
I'm not sure when you installed that, but the nwere 0.8.x versions of Bitcoin-Qt are quite a bit faster than the older versions. They still take a few days to synchronize the entire blockchain after the intital installation.
You are relying on trusting the peers you are connected to to do some of the transaction validation for you. How much trust you are placing in them depends a bit on which "lightweight" wallet you chose.