Exchanges determine price by matching bids and asks.

The modern processes for this are called Auctionmarket and Level 2.

Bitcoin itself does not provide a "price" (Some people prefer the expression "Moscow Time"). The multiple exchanges around the world do. You can trust this process since if the price was misquoted or suppressed at one exchange there would be an arbitrage situation that would balance itself out.

You can also assume that there isn't a conspiracy by exchanges to suppress the true value of Bitcoin in fiat because that would mean that are lot's of unmatched bids & asks somewhere - then any local Bitcoin meetup behind your favorite pizzaria in town would trade at vastly different levels. The market ... always finds a way like a drop of water to the ocean.

Finally, exchanges do not have to be decentralized like some shitcoiners pretend to need. Bitcoin is a decentralized world - the access to it can not be guaranteed to be decentralized like Diagon Alley is the access to the magical world in Harry Potter - but isn't the magical world itself. (I hope that metaphor makes sense). The market itself is decentralized every time you buy/sell/work in Bitcoin in the real world or every time you exchange Bitcoin in your local Bitcoin meetup behind your cities pizzarias - capitalism , markets and arbitrage do their magic on their own.