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How is the actual trade on exchanges processed for simple stock orders?
The simple answer is, there are many ways for trades to take place.  Some systems use order-matching software that employs proprietary algorithms for deciding the order of processing, others use FIFO structures, and so on.  Some brokerages may fill customer orders out of their own accounts (which happens more frequently than you might imagine), and others put their orders into the system for the market makers to handle.  There's no easy all-encompassing answer to your question, but it's still a good one to ask. By the way, asking if the market is "fair" is a bit naive, because fairness depends on what side of the trade you came out on! (grin)  If your limit order didn't get filled and you missed out on an opportunity, that's always going to seem unfair, right?