How does a stock exchange work?

Can you elaborate on the workings of a stock exchange in a concise manner? I'm particularly interested in understanding the key processes that facilitate the buying and selling of stocks. For instance, how does a trader initiate a transaction? How are prices determined for a particular stock? And what role does the stock exchange itself play in ensuring the smooth operation of the market? Additionally, how are the interests of investors protected within this framework? I'm keen to gain a fundamental understanding of the mechanics that drive this crucial financial institution.