Swipe down from the top of the screen, select Settings, press Data usage and then flick the Mobile data switch from On to Off - this will completely turn off your mobile data connection.
Note: you will still be able to connect to the internet and use apps as normal if you are connected to a Wi-Fi network.
If you want to set a limit for how much data your Android smartphone uses over the course of a month (or any time period), plus a warning that tells you when you are approaching that limit, once again visit Settings > Data usage. Make sure the monthly usage cycle matches that of your phone contract (don't assume it refreshes from the 1st of each month).
You will see a large graph detailing how much data you have used over the course of the month. Choose a maximum amount of data that can be used in a month, and when Android should warn you that you are close to that limit. Drag the two horizontal bars across the graph to reflect these choices.