Using an exchange is likely the most common way people get bitcoins. Exchanges are business that broker trades between people. The buyers and sellers using the exchange set the rates by putting in an order to buy or sell.

This is best directory of exchanges that I've been able to find. https://en.bitcoin.it/wiki/Category:Exchanges

Exchangers are businesses that sell (and buy) bitcoins to the public and set the rates themselves. These are likely the next most common way people buy bitcoins.

This is the best directory of exchangers that I've been able to find. https://en.bitcoin.it/wiki/Buying_bitcoins