Bitcoin may be sold and bought through an exchange site or through a broker or individual trader. Which exchange site you choose or which broker you trade with will depend largely on where you live or work, as funds will need to be transferred easily and locally without the need for expensive currency conversions and international telegraphic transfer fees.
You may refer to Buy and Sell Bitcoin by Country and Geographical Location to select the exchange closest to you. Note that most exchanges require that you submit some personal documents in order to comply with Know-Your-Customer (KYC) and Anti-Money-Laundering (AML) policies and regulations. All standard procedures which you should find no difficulties with.
It is also advisable that you have a bitcoin wallet set up and ready for you to transfer and store the purchased bitcoin, as it is always safer to be in control of your own bitcoins than leaving it at the exchange. You may refer to Setting Up a Blockchain Wallet on Web Browser and Mobile Devices to get started immediately, or while you wait for the exchange to verify and approve your account identity.