I've been trying to figure out how bitcoin exchange services work. Specifically the ones that allow you to exchange btc for fiat money and viceversa.[/q]
They allow people to send money (both BTC and fiat) to them. Then they allow people to buy bitcoins with fiat (if they have deposited enough fiat) from other people who want to buy fiat with bitcoins (if they have deposited enough bitcoins).

Exchanges don't actually buy or sell fiat or bitcoins themselves, they're just a marketplace who brings together people who want to trade. That's the service that the exchange "sells", and for which they charge a commission fee.