There are two ways of acquiring ether:
- Acquiring it from the block reward from mining
- Acquiring it from someone else
The first option is too complex and costly for newcomers.
The latter requires a market for people to buy and sell ether. This is where exchanges come into play. Exchange are a place where anyone can create sell orders and anyone can fill those orders, acquiring ether. You can of course give cash to someone for ether, but that's risky and harder to trust the seller.
There are centralized exchanges where the exchange has complete custody of your funds and they own the private keys so technically they own your funds. The pros of centralized exchanges are that you can do fiat to crypto trading because they comply with money transmitter regulations and typically have simple user interfaces for newcomers to start trading right away. When you do trading within a centralized exchange, each trade is instantaneous because it's just keeping an internal ledger of the transactions, kind of like having a tab open at the bar. It's never making any transactions to the network unless you're withdrawing to an Ethereum address. The cons of a centralized exchange is that they're extremely vulnerable to hacks and heavy monitoring and possibility of closures by the government. Centralized exchanges also have higher fees because of the convenience they're providing. An example of a popular centralized exchange in the US is Coinbase.
There are decentralized exchange where you're in custody of your own funds and you create orders by creating a signature of the order (maker/taker pairs) and either store the order in an off-chain orderbook or broadcast it through events on the ethereum blockchain. Then someone can become the taker of the order and fill it by making a transaction with the order and the order's maker signature. The coin transfer occurs through a smart contract. Decentralized exchange don't interact with oracles because it needs to be completely independent of 3rd parties, so they're limited to only crypto to crypto trading (no fiat). Decentralized exchanges also tend to be more complex and have a slight learning curve for newcomers. Example of some popular decentralized exchanges are EtherDelta and 0xProtocol (relayers).
Decentralized exchanges require ether for gas costs so typically people go through a centralized exchange to acquire ether from fiat in the beginning and then move to trading on decentralized exchanges for other tokens.