When I buy a Bitcoin with dollars, where does the money go to? I understand the networking concept of the coin, but I am not sure I understand the purchase process.

Let's say I have 1000$ that I want to spend on Bitcoins, who do I give this money to?
You give the money to someone who has bitcoins available to sell to you.

This might happen via an exchange such as bitstamp.net which matches buyers and sellers.