Bitcoin is the world's first cryptocurrency, and any central authority does not control it. Bitcoiners can transfer Bitcoins via peer to peer network, and these transactions are tracked on a Blockchain, which is called a ledger. It records every transaction.
There are various ways to buy Bitcoins, and some ways are more secure than others. You can buy from crypto exchanges, which allows the option to buy BTC from major fiat currencies. There are some most popular cryptocurrency exchanges which will let you buy Bitcoin like Coinbase, Gemini, CEX.IO, BitStamp, etc.
All the exchanges have different requirements, and the normal process is to register yourself and buy Bitcoins from the exchange. Registering for an account needs you to submit a few personal details like name, address proof, etc. You also need to provide your payment details to fund your account. Verify your email and phone number while also completing the KYC, and you are ready to buy Bitcoins.