Find a Direct Seller over the Internet
Some websites offer an option to search direct sellers: LocalBitcoins, Bitcoin OTC or the Currency Exchange Forum Section. If you find someone who wants to sell bitcoins, you can send them fiat currency (USD, EUR, GBP, AUD), using any payment method, for example, PayPal. However, if you choose this option, you have to trust a stranger. If you think that someone is shady, ask an admin or a moderator about your doubts.
LocalBitcoins is one of the most trusted online exchanges.
At LocalBitcoins, you can sell bitcoin online via PayPal. At the same website, you can buy bitcoins with fiat currency transferred from your PayPal account.
Once you log into LocalBitcoins, you can select from various options: Money Bookers, cash, bank transfers, debit cards, gift cards and a range of online wallets. The site features the price that each buyer offers, and the payment method (PayPal). The buyer can add the terms of trade, for example, they may ask you to prove that your PayPal account is verified. They may describe their business approach, their offers and options.
LocalBitcoins has a Bitcoin escrow option, it holds your money until you finish the transaction.
Virtual World Exchange
PayPal does not allow you to buy bitcoins directly. Sellers are taking chances when they sell their digital currency. Bitcoin buyers can perform chargebacks. There are lots of hacked accounts out there, which PayPal will freeze as soon as they notice them. Besides, Bitcoin and PayPal are online payment methods that compete for an audience, so PayPal does not support bitcoin. Since September 2014, PayPal works with bitcoin related sites - GoCoin, Coinbase and BitPay.
You can still use Virtual World Exchange as an intermediary. PayPal accepts Second Life Linden, another digital currency. You can buy SSL through PayPal, and you can sell your SSL for bitcoins. This transaction requires higher fees than other transactions.
Security: Be Reasonable and Cautious
Bitcoin is fast, convenient and does not have plenty of verification steps, which means it is less safe than other, regulated systems. You do not know the third party, the people who buy your currency or sell currency to you; and the site will not require them to verify themselves.
When you turn to an online exchange, you take risks. You cannot know whether the clients who buy your bitcoins are respectable persons. Do not exchange or store large amounts of money via unknown third party. Moreover, the operator of the website might disappear with your funds. Probably the system is not secure enough and electronic thieves may find their way to your money. Before you start using an online exchange, do some research on the operator of the site. Is their real life identity available?
Seek for reviews of the previous clients of the online exchange. At least, do some Google Search on the website and the operator or company behind it. You can find useful information on the Bitcoin Forum.
When you turn to banks, you have less chance to stay anonymous. If you are looking for anonymity, buy bitcoins locally, pay by cash, or post cash in mail. However, you still face the risk of losing your money.