You haven't mentioned the type of phone - Android, Apple or other - but, in general, if you have access to your wireless router at home, that's the best way to connect. You'll have the benefit of the full speed of your home broadband service. There's no additional cost involved and you aren't using up your data allowance.
When not at home or somewhere that allows you WiFi internet access, then you need to use the phone's "mobile data" service. Depending on where you are, the connection may be 2G (GPRS/EDGE) or 3G (3G or HSDPA). An Android phone will indicate the type of connection you've got with the symbols G, E, 3G or H.