Before the internet
We were, I suppose, lucky. The internet as we know it was non-existent when I had to worry about my children. There were things to worry about, though - sex, drugs and heavy metal for starters.
One problem is that we keep talking about "children" as if they are all alike, but there are huge differences between seven-year old children and fourteen year old children.
When they're seven, you can ban computers in the bedroom, and control mobile phone access and screen their friends. Come fourteen and they head out of the house, "Where are you going?" "OUT". And you have to decide whether you are prepared to make an issue of it. I didn't, but I was prepared to make an issue out of what time they came in - and spent 2 years of my life on a permanent war footing. And discovered that they had more stamina than I had, and more relish for the fight.
On the other hand I never had many worries about alcohol - I knew they would get drunk from time to time, and doubtless regret some of what happened as a result. But I had let them sample wine/beer at mealtimes since they were quite young and they largely despised those of their peers who went crazy the minute they could get into a bar.
I suspect that, as other posters have suggested, that the only way to handle this is education. But you have to do it early enough. They learn a lot very young these days, so you might as well take advantage of that knowledge.
If they know what porn is before they really want to access it, then you can talk to them about it before [a] they find it too excruciatingly embarrassing to talk to their parents about sex and [b] they want to make a point of conflict, because fighting their parents is what teenagers do.
[Pundit mode]The worst damage that porn does is not that it makes innocent children think about sex, when they would otherwise be pure in heart and body, or even that it gives them the wrong signals about acceptable bounds of behaviour in real life. The latter will usually correct itself . It's that they can end up with totally unrealistic ideas and ideals about their own bodies and the opposite sex, and sexual performance and that can cripple them for life. Most porn is about as realistic as World of Warcraft. You can't just teach them (or try to teach them) not to use the stuff - it's a learning ground for many young people. You can teach them to distinguish it from real life.[/Pundit mode]
But they will fight you, and try to outwit you about something - that's part of growing up for most teenagers.