This has been mentioned in other comments, but I thought it would be good to highlight it further: the answer to this question is exactly the same that for any other commodity.
Commodity means an asset that is highly fungible, i.e., you can replace two items of that type for one another entirely or almost entirely. Examples of fungible assets besides bitcoins include dollars, stocks of a given company, gold bars, crude oil or rice. Examples of non-fungible assets include houses, works of art and, unsurprisingly NFTs.
And as other answers mentioned, commodities are traded in exchanges, which are basically systems for matching buy bids (each of which sets a maximum buy price) to sell offers (each of which sets a minimum sell price). Exchanges tend to be few and large since the more buyers and sellers in a given system, the faster you are likely to get your sale through.
In any such exchange system, all we can know is what buy/sell offers people have made, and then try to come up with a decent "value" from this continuous stream of bids using some algorithm. A broker might then use such algorithm to set their price for a given commodity so that less specialized/smaller buyers can buy more conveniently, but ultimately the broker will be selling commodities they bought with that ever evolving offer system.
Of course, if someone buys too high, or sells too low, they will lose money so the price tends to be metastable around a given value in the short term, until other external factors alter the value perception. But there can also be a tradeoff, as buying high and selling low also mean you will get the trade faster in case you need the money urgently for something else, or if you've learned before others of some information that implies that the asset value will fall dramatically in the near future. A good example of that can be seen in the movie Margin Call about the 2007 financial crisis.
I think the only guarantee that traditional exchanges are not rigged by hiding/delaying information for someone's benefit is trust in their reputation and legal repercussions of doing so should they be caught. One thing that people who don't feel that this is enough could do is try to do create more decentralized systems, e.g. Ethereum based. The most notable one appears to be Uniswap (thanks to Boris in the comments). Wikipedia mentions that:
Uniswap’s average daily trading volume was US$220 million in October 2020
and their daily volumes are reported at: https://info.uniswap.org/#/