To spy on your child's cell phone, call or go into the mobile carrier store connected with the cell phone. All major mobile companies offer tools or apps to track cell location, block downloads, prevent texting while driving and limit data usage or time spent on the phone.
Another option is to visit the app store attached to your cell phone's operating system. Parents can download apps to their children's phones that connect to their own phones or computers and display how much time the child is spending on the phone every day. These apps also allow the parent to set up schedules for blocking use during school or after bedtime. Some of these apps show which apps have been installed previously and limit the time spent per app on a daily basis.
There are other apps you can download to monitor a child's social media and text messages. Most of these apps are not free, and some have a monthly subscription fee. These apps operate in the background of the phone, so children don't know they are active unless told. Some apps block certain numbers from contacting a child's phone, and other apps keep track of attempted calls or texts by the child or the blocked number.