Who decides what a share costs right now?

Nobody sets a share's price. It comes out of the interactions of buyers and sellers, a process economists call price discovery. On a stock exchange, those interactions happen in a list called the order book: one list of buy orders and one list of sell orders for each stock.

Each buyer says the highest price they will pay, called a bid, and each seller says the lowest they will accept, called an ask. These are limit orders: an instruction to buy at no more than, or sell at no less than, a specific price. A limit order gives you control over the price, but it may never be filled. The highest bid and the lowest ask sit at the top of the book, and the gap between them is the bid-ask spread.

A deal happens when the two sides meet. If a bid is equal to or higher than the lowest ask, those orders are fulfilled at once and leave the book. Someone in a hurry can place a market order instead, which is executed immediately at current prices, putting certainty of getting the shares ahead of the price. In a fast-moving market, the price they get can be quite different from the last one quoted.

So the spread is a price for speed. An urgent buyer and an urgent seller are separated by it, and whoever demands immediate action pays it, while whoever waits with a limit order earns it. A market maker, a firm that quotes both a buy and a sell price, hopes to earn exactly that difference.

That is why "the price" of a share is really a snapshot. It reflects where buyers and sellers meet at one moment, the market's view of the future in a single number.