Pick Jayce, Jax or Darius. Poop on your lane, and any time wave is pushed or they're B, go try to find their jungle and kill them in their jungle or gank mid. If mid and jungle aren't around, steal camps and go back to pooping on their top. Take tower early and roam if you know what you're doing. If the other jungle is camping you, even if you can 1 v 2, it means you are spending too much time in a gankable position attempting to harass/kill their top rather than exercising your power on mid and that half of the jungle.
tl;dr Kill the other top early and/or deny them farm, then start roaming your half of the map hard and snowball the game while they try to catch up.
Note that everyone of these things is extremely difficult to do. You'll still need one other person to be decent. You can't carry if the team refuses to even get on your back. Any hard carry usually has one other person who will be useful to you. That's been the case in every carry I've ever had. Which is why everyone says Duo.
How do people like Dyrus do this? 100 percent of the time my mid and bot do absolutely terrible, and even if I got 8/0 I am still unable to carry my team. I am not complaining about the other lanes, I just want some tips on how I can carry a team that is doing extremely poorly? Should I just keep pushing? What if the jungler just camps my lane and my jungler just continues to farm the jungle? How do I make a play by myself?
I am basically asking for things that I can do. Assume that my teammates do nothing, and will do absolutely nothing to help me accomplish an objective. Because I just had a game like this.
Starters he doesn't really ever carry a team as top. It happens once in a awhile in his stream. He does however win lanes 60-70% of the time and when he don't win his lane he at least slows down the top while doing it.
If their jungle is having a camp out, then don't push stay just out your turret range and farm their. Once you get ahead push to tower, go help mid or counter jungle their top jungle. Return to farming top and repeat. If needs be let them take tower down if you can't seem to farm so that you can farm easier and setup ganks easier. Ward river and maybe even their golems or red and gank their jungle there if possible. Top can't carry like adc and mid can its harder to do. Make use of your being ahead, buy a item with armor or MR depending on who on their team is doing the best. Helping the lane that is doing the worst will help get them ahead too.
The secret to winning game from top lane is to not stay top lane.
It doesn't matter in the slightest how fed you are if you aren't putting that to use. Killing the enemy top over and over doesn't achieve anything. It's their bad player keeping your teams good player busy, that's a win in their book.
Take teleport if possible, Push hard, get 1-2 kills early, take top, and GTFO. Go murder mid a few times, bot a few times, counter jungle. Don't sit top and farm.
You can't just leave top totally, you need to go back to push, gank top. If you do it right their jungle will have no choice but to always be close or you just push, push then are free to roam which they don't want to happen. By being in lane to push you can roam and you are keeping 2 people busy allowing most fights to be 4v3 or else they loose a tower/inhib if jungle or top go to help. It works both ways, but you need to know when to be in lane and when to be ganking.