There are many different exchanges which you can signup to. The signup process varies between them all, but you will need to supply them with your identification to prove you are who you say you are. This can be a lengthy process depending on the company you go with. Once you are approved, however, you will be able to deposit money and buy bitcoins.
Here are some good exchange options if you have fiat currency like USD, CAD, Euro, etc:
If you have other forms of cryptocurrencies, then you can exchange them for bitcoin at this exchange: