Some ways of getting stock market quotes include watching a ticker, Googling individual stocks or looking at the landing page of any of various financial websites. There are also a few apps that allow you to check the stock market from a phone or tablet.
According to Investopedia.com, learning how to read a ticker tape keeps users aware of various stocks in the stock market. Looking up the stock name on the ticker will alert users to the stock valuation (the price the stock is being traded at) and the change amount (whether it has gone up or down). Google searches can reveal this same information.
Real-time quotes are available on CNBC's Stock Screener. A market overview and stock quotes can be obtained from the main landing page of Investopedia.com.