What counts as verification or validation of a transaction? 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.