TT tower pushing you just push. Like find a tower you want to push, make sure nothing strong is at stake like Dragon, and go push it. If they send 3 people to defend, depending on your team you can say **** em and tower dive, you can let the wave reset back closer to the middle and then split push, you can move as 3 into the jungle and wait to ambush them. If they don't ward a lot, they can't cover the threat of pushing while you clear out the jungle while potentially clearing out the other lane as well. They will fall behind in farm unless they can do what you do, but better, or if you're doing something like farming bot jungle and they get top for free.
Typically, if you have clearly won a team fight, you use that time to push. If you're too weak to secure dragon/dragon isn't in the picture, you push. If it's super early game and death timers are low, you farm/clear jungle safely go back and come back with item advantage. If both teams are in a stalemate, you either gotta hope you ambush someone/get a good initiation on a fight, or hope you have the better comp for down the road.
You can also try push orientated comps. Some **** like Heimer blah and blah. Throw down turret to take additional aggro, use free time to get free pushes, when enemy team comes back off.