Buying Bitcoins today is actually quite easy, first you need a bitcoin wallet to store your Bitcoins once you buy them, then you need to find an exchange to buy from which there are plenty of. For newcomers to Bitcoin I recommend using Electrum because it is easy to use and easy to recover your bitcoins, there also is no waiting or down time. Coinbase and Circle are two exchanges that function very well and are actually quite similar.
Most exchanges require you to verify your identity, it usually requires a bank account and an id. Every exchange is a little different but overall it is an easy process, Circle and Coinbase require a bank account and the last four digits of your SSN (be careful which exchanges you give this out to, before I even added my bank account to Coinbase or Circle I did background research to play it safe.) And all the reviews were great, usually you’ll notice if an exchange isn’t safe.
Once you buy your bitcoins you can either leave your bitcoins in your exchanges wallet, which makes it easy to sell them if the price changes. But keeping your Bitcoins in a web-based wallet isn’t the best idea unless its insured or have top-notch security; as security for web based wallets are sometime lacking and they bigger targets for hackers.
The safer and more secure option is to put your Bitcoins in a wallet that is 100% by you, the downside is that if you forget your encryption key or lose your recovery seed then there is nothing you can do.
Selling Bitcoins is just as easy, just repeat the steps backward. Send them to your bitcoin address that they provide and in a few minutes they will be transferred. If you keep them in your exchanges wallet then it will be even easier to sell and there wont be a transaction fee. A transaction fee is a small fee, the price of the fee varies depending on the size of the transaction.