As Cardano is one of the most popular coins, many of the well known exchanges and sellers list it.
Some of those are Binance, Coinbase, CEX, eToro, Coinmama,…
You will need an account at the exchange you chose to buy crypto. The registration process depends on the exchange. Due to regulations and anti-money laundering rules most of them will require you to provide personal details and verify your identity before allowing you to buy cryptocurrency.
In the process of buying ADA you will be asked for a Cardano receiver address which you can get from your ADA wallet (Yoroi, Daedalus,…).