Exchanges
Cryptocurrencies can generally be sent between two parties without intermediaries, which is also one of the biggest benefits of using them. In the origin of Bitcoin, you simply had to pay in cash, after which a kind soul sent Bitcoins in return.
Of course, this was not very effective, and it was not possible to get any knowledge of the actual market value of the currency. The risk for fraudsters was also extremely high. It did not take many years before exchanges came where you could buy and exchange bitcoins and other currencies.
One of the first exchanges was Mt. Gox, which with great success let a lot people own Bitcoins for the first time. They later happened to be hacked and lost 750,000 Bitcoins (7% of all existing bitcoins), and in 2014 they went bankrupt. A large number of people therefore lost their bitcoins at an early stage.
Cryptocurrencies themselves are secure, as long as the private key is in safe custody. But having your money on a exchange always involves a risk. It is not your money if you don't own the key, exchanges then function as a bank. The media often incorrectly reports that "Bitcoin has been hacked", which has never happened. What is meant is that a large exchange has been hacked.
How it works
Most exchanges still don't accept money by credit card or bank transfer, because they do not want to be confused with a bank - with all the rules, laws and obligations this entails. The largest exchanges do, like Coinbase and Binance.
The smaller exchanges, on the other hand, require that you already own another cryptocurrencies, which you send to your wallet at the exchange. It is common to have bought Ethereum from someone who receives money from your bank, and you then send these to a smaller crypto dealer where you can exchange Ethereum for something else. It means hassle, absolutely, but this hassle means that those who have the strength are one step ahead of everyone else.
Large exchanges
Binance
Today Binance is the largest exchange of cryptocurrencies. They let you buy currencies with credit cards and have a large selection of currencies.
CoinBase
The second largest exchange has great interface, and is known as the simplest of them all. They accept money from international bank transfers and credit cards, but are also known for large fees. They have fewer cryptocurrencies than Binance for example.
KuCoin
The interface is cumbersome, and they require you to already have cryptocurrencies to trade. But they have many currencies that are not found on either CoinBase or Binance.
Decentralized exchanges (DEXes)
A regular exchange is centralized in the same way as a bank is. They have large sums of cryptocurrencies, and when it says you own 10 ETH, it's their database that says they owe you this. They keep it for you. When you buy more of a currency, there is probably no change on the blockchain, but only in their internal system.
This is not how it works in a decentralized exchange. There you verify with your wallet and you buy and sell currencies directly between two parties, without it going through an intermediary.
Most people today still have their order list centralized, but new players in the market such as UniSwap have solved it through liquidity pools where users put in coins and tokens where they can then be bought up by another party. They thereby earn a percentage because they contribute to the pool.
Many believe that DEXes will take over the cryptocurrency trade more and more in the future, as they follow the same ideology as the cryptocurrencies themselves. Ie no intermediaries, and full control to the individual. In general, they have alot of small, obscure cryptocurrencies that others do not have. DEXes have increased significantly during the year 2020 and 2021.
Examples of decentralized exchanges today are UniSwap 1inch, Kyper Swap, Binance DEX and IDEX.