Who decides the price of a stock?

Nobody, which surprises a lot of people. There is no committee and no company official setting the number. The price you see is simply the most recent trade: the last amount at which one person agreed to sell and another agreed to buy.

At any moment there is a list of people willing to buy at various prices (bids) and people willing to sell at various prices (asks). When a bid and an ask meet, a trade happens and that becomes the new price. The gap between the highest bid and lowest ask is the spread, and for big stocks it is a cent or two.

So when a stock "goes up on good news," what actually happened is that the news made more people want to own it than sell it, buyers had to offer more to find willing sellers, and the trades started printing at higher numbers. The news did not set a price; it shifted the crowd.

The exchange’s role is to match those orders quickly and fairly. Market makers, firms that constantly quote both a buy and a sell price, keep it liquid so you can trade at any moment without waiting for another individual to show up.