Smartphones are designed to access the Internet and download information using cellular service towers, just like voice and text messages. However, using Wi-Fi for data won't impact the monthly usage costs.
Cellular phones today are often bundled with data plans as part of the basic package of service. Most carriers place a limit on how much total data transferred over their network a customer can download in a given month. Some plans do include unlimited data usage, but it is possible with most phones to avoid paying for this service completely simply by accessing the Internet at known Wi-Fi hotspots.