I understand the general ideas and properties of the block chain, but have not been able to understand how a transaction is created and gets to be verified or validated.
A transaction is a output generated from a end-user's wallet software. It contains their address, the recipients address, and the amount to be transferred (among other things). After the wallet creates the transaction it then broadcasts it to the peers you are connected to and is added to a queue to be confirmed. The world will know, semi-immediately, that you have broadcasted this transaction, with a current status of unconfirmed. The transaction can now be viewed on a blockchain explorer with the txhash that was generated (a unique identifier of that transaction).
Miners confirm transactions in the queue by expending electrical power and processing power. After a transaction has been confirmed it is then added to a block. Once the entire block has been generated and confirmed, the transaction then stands at one confirmation.
Different sites and services require a varying amount of confirmations before doing certain actions.
A transaction is created when a Bitcoin client on a personal computer, smart phone, server, etc. creates and broadcasts a new transaction to the rest of the Bitcoin network.
At this point, the transaction will be propagated relatively quickly to the (currently) 5,400 or so Bitcoin nodes that make up the Bitcoin network, of which a certain percentage are also miners.
The transaction is not confirmed until a miner produces a new block that contains the transaction.
To be technical, many nodes do validation and will reject any transactions they do not consider valid, but only miners do confirmation.
So with regard to the additional term verified as used in the original question, it depends what the definition of verified is.
Every time you send bitcoins you have to reference the transaction(s) where you got bitcoins from. That previous transaction also has to reference the transaction(s) it got bitcoins from. So on, and so forth, all the way back to the transaction where the bitcoins were created.
At each step in this history, the previous owners provide a digital signature that shows they approve of the transfer of funds. Each signature has to be checked, to verify that the owner approved of the transaction. Full nodes keep a database of verified transactions, so that they don't have to recursively verify the whole history of a transaction.
There are a few other things checked for in a transaction, that it's not too big, and that amount of funds spent by the transaction is at least as much as the amount given, for example, but the main work in verifying a transaction is checking the digital signatures.