Assuming that you have already invested some money in Bitcoin you need to decide now how to make them safe.
Bitcoins are associated with an identifier called an address which is an alpha-numeric string. Every Bitcoin address consists of a public key and every public key has a corresponding private key. With the private key you can prove that you are the owner of the Bitcoin address and you can sign transactions to spend the bitcoins.
If someone steals your private key, he has full access to all the bitcoin connected to that address. Needless to say, you need to figure out how to secure it.
Example of a Bitcoin address: 1CC3X2gu58d6wXUWMffpuzN9JAfTUWu4Kj
Example of a private key: 5Kb8kLf9zgWQnogidDA76MzPL6TsZZY36hWXMssSzNydYXYB9KF
Example of a public key: 0450863AD64A87AE8A2FE83C1AF1A8403CB53F53E486D8511DAD8A04887E5B23522CD470243453A299FA9E77237716103ABC11A1DF38855ED6F2EE187E9C582BA6
The private key and public key are stored in a wallet. Wallets can be either offline or online.
An online wallet is, as the name suggests, online. The private keys are on the internet. You must choose to trust a third party that takes care of your keys. You trust that they do not run away with them or get hacked.
The online wallet service inputs.io got hacked and their customers lost a total of 4100BTC.
I don’t recommend using an online wallet for any larger amount of money. It is more suitable for smaller amounts intended for spending because its accessible from everywhere you have an internet connection. One online wallet that has good reputation is the open source blockchain.info. There is another open source service called coinpunk.com that currently is in beta, but it has great potential.
An offline wallet is a wallet that is generated and stored on an offline computer to minimize attack surfaces. Offline wallets provides the highest level of security for your bitcoins. To get started, download a wallet application and transfer it to an offline computer via an USB-memory. There are many wallet applications, but the most secure and stable ones in my opinion are armory and electrum.
To be completely safe I recommend using a clean install of Ubuntu (remember to check md5 hash) with the network card physically removed. That way you minimize the possibility of having malware on your computer. An excellent in depth tutorial on how to do this can be found here: http://falkvinge.net/2014/02/10/placing-your-crypto-wealth-in-cold-storage-installing-armory-on-ubuntu/
As you can see it requires some technical competence to store your Bitcoins at the highest level of security. Even people that have the required background might be hesitant, simply because it is so time consuming.
But there are solutions to this problem. One interesting project is Bitcoin Rezor (http://www.bitcointrezor.com/). It is a hardware wallet that gives the highest level of security for Bitcoins, and is user friendly at the same time. Right now it is under development and the first beta version has been shipped. You might do good to get your hands on one.
In the meantime, you must figure out what level of security you need for your Bitcoins.
Interested in learning about Bitcoin? We invite you to join a Miniseminar on the 6th of march at 8 am in our office in Oslo. In 45 minutes you will get to know the “What” and “Why” of Bitcoin. Free to attend. Talk will be in Swedish, unless the audience decides otherwise. Check and subscribe here.