There are a few ways someone can steal your bitcoins:
The wallet provider If you have any bitcoins they have to be stored somewhere. There are a lot of wallet providers that make it a lot eaiser to use your bitcoins. Throughout the last few years there have been a few wallets that, because they have your private key, just decided to transfer your funds to another account. Some other wallets claimed to have been hacked and to have lost your private key in the process. So one way you can have your bitcoins stolen is if a service has access to your private key.
Exchanges Just like the wallets, exchanges generally have your private key for convenience. It is a lot easier to trade and make transactions if the exchange has your private key. If they get hacked or decide to walk away with your money and shut down operations, there is not a lot you can do. You can find a trustworthy exchange based on reviews and forum comments:
Buying something that does not exist. There is no chargeback in Bitcoin and once you have made a transaction it is irreversible. If the merchant decides to not send you the product you bought and to not send you the money back either, there is not a lot you can do. It's really a scam but in effect they are doing it to steal your Bitcoins.
Anybody that has access to your private key. If you are using a paper wallet someone can steal it from your desk or wallet or wherever you are holding it. If you have your private key on your computer and someone hacks in and finds it, they will have access to your account as well and can steal your bitcoins.
Now, i know all of the above look scary but imagine cash, the ammount of ways you can have your cash stolen and Bitcoin suddenly does not look that bad. Also it's rare that an exchange or wallet would steal your money (it would be similar to a bank deciding to steal money from their customers), it can be done but it's unlikely. Hopefully, as the Bitcoin and cryptocurrency evironment matures, we will see less and less scams/companies that steal your money and more and more serious businesses."