We need 3rd parties to perform certain tasks, for example, you will need an account with an exchange so you can transfer FIAT into CRYPTO, or even between CRYPTO's, e.g., Bitcoin to Ethereum.

Note, coins are getting more and more scrutinized before they are listed on an exchange because of the looming regulation uncertainty, which means they may be on one exchange but not another. Some exchanges already do everything they can to comply with laws in various countries.

Fees vary drastically between exchange platforms.

These are some of the more popular:
https://www.kraken.com/
https://www.coinbase.com/
https://bittrex.com/
https://etherdelta.com/
https://poloniex.com/
https://www.bitfinex.com/

2FA (2 Factor Authentication)
Always use 2FA when using websites that have access to your private information, especially the exchanges. If they don'f offer 2FA, run away screaming (for ice cream preferably).

Enter the wallet

Just like in the traditional sense, your wallet holds your coin. The thing is... they can be confusing, you might need many, and the choices you make should be directly related to security.

TIP: Don't store all of your coins in a single wallet

Hardware::Hosted::Desktop::Mobile (in order of most secure to least secure)

Hardware:

This is the most secure because you store your coin off line and it's hard to lose. You only connect your wallet to a computer when you are ready to make a transfer. Simple! Many solutions come with additional layers of security built in, e.g., a PIN. There aren't too many choices YET but there are many projects in the works anticipating the onslaught of people running to CRYPTO's!

https://trezor.io/
https://www.keepkey.com/
https://www.ledgerwallet.com/

Hosted:

There are good solutions for hosted wallets. Most are easy to use.

Hosted wallets are managed by a 3rd party. It's kind of a cloud service. These are less secure than hardware wallets but probably more secure than a software or desktop wallet. You lose the keys you lose the money.

I imagine the vast majority of these services are doing their absolute best to protect you, however there have been some pretty serious breaches in the past, e.g., Mt. Gox and Parity Wallet just to name a couple.

That said, by leaving much of your security up to a reputable organization is probably better than trying to do it yourself.

Some of these wallets can hold multiple coins, some can only hold coins from the Ethereum blockchain, for example, myetherwallet...

https://www.myetherwallet.com/
https://jaxx.io/
https://www.exodus.io/

Desktop:

Opinions differ vastly when it comes to Desktop wallets. I am in the camp of security because most people do not know how to secure their home computer. Office computers might be slightly more secure but probably for the vast majority of people that isn't enough. If your computer crashes, get's stolen, or hacked, there is little chance of recovery.

UNLESS YOU MADE BACKUPS

https://www.bitcoinarmory.com/
https://electrum.org/#home
https://metamask.io/
https://bitcoin.org/en/download

As always, everything in this article is my opinion and I welcome all comments.