The name “Bitcoin wallet” is a bit of a misnomer. Bitcoin wallets don't hold actual Bitcoins, those are essentially stored on the blockchain. Instead, Bitcoin wallets hold the private keys that give users the right to use those coins. Each Bitcoin wallet comes with at least two keys (multisig wallets can have more) one public, and one private.
The public key lets any Bitcoin user send a sum of Bitcoins directly to any other Bitcoin user, without a middle man. The private key must be kept as secure as possible, since anyone who gets a hold of it has access to every Bitcoin associated with it.
There are several types of wallets out there: Software wallets, web wallets, and paper/cold wallets. This guide will hopefully help you understand each of them.
A software Bitcoin wallet is a wallet installed on your actual computer that you actually control yourself. Ideally, only you have access to the private keys that store your Bitcoin.
Getting a Bitcoin software wallet is as simple as picking which wallet you would like to use and downloading it. Bitcoin Armory is the most popular, stable and secure software wallet. It is also open-source, so the community can make sure their claims aren't full of hot air.
There is also BitcoinQT/Bitcoin Core, which is the original software Bitcoin wallet, and Multibit, which has the advantage of not requiring that the entire blockchain be downloaded.
That blockchain download is the main barrier to using a software wallet. It is required downloading for any locally stored software Bitcoin wallet. The file size currently sits at 18GB and is growing.
Software wallets provide more security than web wallets but greater accessibility than offline wallets. However, they are only as secure as the computer they are stored on. Malware is beginning to attack Bitcoin holding computers specifically. If a computer is compromised, any private keys may be as well.
Once you download the wallet software, it will synchronize with the network by downloading the blockchain. That will take a few hours but once that is done, sending and receiving Bitcoin is as simple as clicking the appropriate buttons and following the on-screen prompts. Of course you will need to know your public key (for receiving) and the recipient's public key (for sending).
Paper wallets are the closest thing Bitcoin has to a physical form. Private and public keys can be printed out or even written down, and so long as the computer data that stored that information is deleted, no one can get to it.
The popular web wallet services, like Coinbase and blockchain.info offer a service that make it easy, but if you are the paranoid type you can go to bitaddress.org and create one yourself. Either way, once Bitcoin is “moved” to a paper wallet, no nefarious parties can get a hold of it without getting access to that slip of paper.
Using the public key, you can send more Bitcoins to the paper wallet without bringing it back online. However, if you want to spend any of that money, you will have to bring the private key back online and “sweep” the account into an online or software based wallet.
The advantage of paper wallets is that they essentially store your Bitcoin on a physical piece of paper, removing it from the digital world and safeguarding it in the physical one. This makes them essentially unreachable for spending until they are brought back online, but it is the most secure way to store Bitcoin long term.
The most convenient Bitcoin wallet is web wallets or online wallets. These are run by third party companies that make it easy to access your Bitcoin to purchase items or quickly trade Bitcoin. The trade off is having to trust a third party for your Bitcoin's security.
Web wallets vary in function and capability. Coinbase prides itself on usability and merchant services, as well as integration with fiat services, including bank account and credit/debit card integration. Blockchain.info is a popular open-sourced hybrid wallet that gives a nice mix of security and convenience. BitGo and Greenaddress are two multisig wallets and Coinkite is similar to Coinbase, but with a suite of hardware designed to help Bitcoin become prevalent in the real world as well.
At this point, a quick explanation on multisig (multiple-signature) wallets will probably be helpful. Multisig wallets require two or more private keys before the coins can be released. This adds more security and can potentially be used for all sorts of interesting uses, like shared accounts and business contracts. Expect multisig wallets to become a huge part of the Bitcoin ecosystem over the coming years.
As mentioned, web wallets add a level of convenience that software wallets can't such as being able to access your funds from any device, for example. But keeping Bitcoins in an online wallet is a bit like keeping them in an uninsured bank in the old American Wild West. So long as the wallet/exchange remains secure, so will your Bitcoins. But, if something goes wrong, there are little to no options to get your Bitcoins back.
You may have also heard something about “Cold wallets” elsewhere online and wondered what those are. Cold wallets are simply any kind of Bitcoin wallet that isn't connected to the internet. It can be a paper wallet, which we discussed above, or a software wallet stored on a USB drive or other removable storage device. These wallets are also kept offline, but can be brought back online without “sweeping” the entire account like in Paper wallets. The blockchain will have to updated or downloaded (depending on if you stored the 18GB file on the removable device or not) but getting it back online is a fairly straight forward process.
There is also a thing called “brain wallets.” A computer makes up a pass phrase of random words that the user commits to memory. That pass phrase can be used to regenerate a Bitcoin private address. The pass phrase can be written down or memorized, but like a private key, anyone who has it, has access to the wallet's Bitcoins.
Hardware wallets that can only be accessed with physical contact to the wallet have hit the scene this year, although they tend to be back ordered pretty heavily. They essentially work like a USB stored wallet or as a way to securely keep track of several paper wallets.
Bitcoin is a “trustless” system, meaning you don't have to give every merchant the information they need to steal your money every time you use it. This fundamental function makes Bitcoin inherently safer than fiat currencies. However, as with any new, confusing technology, there are an increasing number of fraud attempts and scam artists lurking through the internet, looking to steal a few Bitcoins. Thankfully, Bitcoin has more than a few options to give each user the right mix of security and accessibility.