Its really not that hard. There are alot more players than i’ll hit on, but at 30,000 feet lets look down. The stock market is a place (that can be a single physical location like the NYSE) or no single location, like the nasdaq. The stock market receives orders from clients to purchase shares of stock in a company, say GE (general electric). That order, is given to what is called a runner. The runner takes the order to a trader. The trader goes to the specialist (one who matches up buyers and sellers and is the seller or buyer of last resort if there are no other sellers or buyers), the specialist takes that order and matches it with someone who wants to sell. You see, all the stock market really is, is a place where buyers and sellers are matched.
While what i told you is correct, it does not count every single step and does not name every player, it should give you a pretty good idea how it works. I hope this helps you.