Someone correct me but my understanding is this:

think of it like a stack of buy and sell orders.

when somebody want's to buy, they will buy from the cheapest sell order. But there is a limited number of units at that price. So as that supply is exhausted, people will have to pay a higher amount for the more expensive sell orders (which are now the new cheapest).

The more people trying to buy, the bigger the demand, and the faster those orders will be chewed through. Leading to an increase in the price.

This works in both directions.

as for:

"who is the authority I ask for setting a price?".

The price is whatever you can sell it for (i.e. what somebody is willing to pay for it). Which corresponds with the buy/sell orders I mentioned. I imagine google or whoever google gets the data from are just processing that data and pooping out an about right figure.