I think you should reevaluate invading your child's privacy like that. Would you want your parents doing that?
However if you must the only way to do get into the phone, and see what is currently on it is to wipe and restore the device. I am assuming you want to know what is on it, not just use it.
First check if the phone has activation lock enabled: https://www.icloud.com/activationlock/
If it does you will need the Apple ID and Apple ID password. AKA iTunes / iCloud account etc.
If it A does not have activation lock enabled or B you know this information you may proceed.
You then have two options for erase and restore, in order to do so there will need to be a backup somewhere.
If you do not have the Apple ID information (There must not be Activation Lock) then you will only be able to do this via an iTunes backup. Check the computer they may sync this phone with. If there is a backup in iTunes (look in the iTunes settings/preferences under devices) Then you can wipe the iPhone and restore it using iTunes using this link If you can't update or restore your iPhone, iPad, or iPod touch - Apple Support
Once you complete that the iPhone should walk you through how to either A restore using iTunes backup or B restore from iCloud.
If you have the Apple ID information you can do either iTunes or iCloud however if you do not have Apple ID info then you can only do the iTunes backup (ONLY IF NO ACTIVATION LOCK)
In the end this will restore everything to the device but omit the password.
I do hope this helps but seriously reconsider doing this and talk to your child instead.