the web browser will have a history of pages he has visited. that's really about all you can view as far as i know. you would need his phone and then need to open the web browser and then look at the history. if he clears his history often though, then there's no way for your to see it. if he is viewing items inside of other apps (picture or video type of apps) then i doubt you can find any history.
Off topic but wabted to help. The only on phone restrictions you can do are settings general then restrictions. It mentions that safari is part of restrictions and if you think he will download things there is an age restriction. Once you set these restrictions you need a password to open it. You can disable the browser if you want to.