There are more or less three options to buy Bitcoins:
A. On an Exchange:
- Open an account on one of the hundreds of available Exchanges (google: Coinbase, Kraken, Abra, whatever you prefer). Also there are many exchanges that target local markets so if you are not in Europe or the USA you may want to find a local Exchange that provides smooth transfers of funds from a local bank account;
- Once you will have opened an account, get yourself verified (proof of ID and domicile are normally required);
- Transfer funds from your bank account to the Exchange;
- Once the Exchange notifies you that the funds have been credited, you can buy Bitcoins.
B. On Localbitcoins.com: open an account and arrange to buy Bitcoins from one of the many local sellers in your area. You can agree to buy Bitcoins in person or via bank transfer and your purchase is protected by escrow. This is very convenient but prices are normally slightly above the market.
C. Work in exchange for Bitcoin: you can work as a freelancer and ask to be paid in Bitcoins, instead of cash. I pay many of my contractors across the planet with Bitcoins, Litecoins and Ethereum and they are all very happy with this.