You open an account with a broker like etrade, ameritrade, schwab. You do that by filling out an account application and sending in your money. An online broker will be the cheapest.
Once the money is in your account, you use their web site to make a purchase or sale. You give them the name of the stock, how many shares you want to buy or sell, and the
type of order.
They'll execute your order and send you a confirmation. That's it.