I need help understanding how this thing works.
Great. What have you read and learned so far, and what do you still need help understanding.
A wallet program generally allows you to see what bitcoins have been sent to you, and to create transactions to send to others.
"Miners" do the work of securing and confirming transactions. They are rewarded with transaction fees and a block reward for this work.
Transactions are relayed throughout the network within seconds. They become very difficult (impossible) to reverse/cancel as they gain confirmations. Confirmations occur about every 10 minutes on average.
Am I able to buy bitcoins out right
Sure. It's a currency. You can provide a product or service and receive bitcoins as payment. You can exchange your local currency for bitcoins (buy them outright). You can beg and hope that someone will donate them to you out of the kindness of their heart. You can scam and steal them. Just like any other currency.
and if so where do I get them.https://localbitcoins.com/https://mtgox.com/https://campbx.com/https://coinbase.com/https://www.bitinstant.com/
You can also look at the Currency Exchange Sub-Forum here at bitcointalk.org
And, you can check out the #bitcoin-otc IRC channel.
I'm sure there are more places as well. These are just some of the more popular ones in the United States.
Someone please explain mining to me. How is it done?
You run a mining program that attempts to find a SHA-256 hash of a block header that satisfies the current difficulty. If you have equipment that can generate a significantly large amount of SHA-256 hashes per second, you can solo mine and get the full block reward for every block you solve. If you don't have as much hashing power, you can join a mining pool and contribute your hashing power to the pool to increase the odds of the pool solving the next block. The pool will then share a portion of the block reward with each contributor.
In general, unless you have access to cheap electricity and/or specialized mining equipment, it tends to be more profitable to acquire bitcoins via other means.