Whatever you're best at! :D
You see, carrying isn't about doing the most damagez or getting the most kills (although those help), it's about doing the best you can to aid your team!
For example:
You're playing support Braum. Now, are you going to babysit your ADC and be a ward bot? If that's what you're good at, then be great at it! But if you want to take a step further, learn how much power a support brings to a team, and utilize different strategies to aid your team. Encourage your ADC to use the blue trinket! Gank a lane solo or with the jungler (I mean, cc is cc, amiright?), ward offensively/defensively, remind your teammates to ward because of the ward limits! Participate in teamfights! Buy utility items as well as tank items! Pinsir the enemy with your ultimate (bonus points if you catch Yasuo offguard)!
The possibilities are endless! Think there's only one way to play every role! Whelp, if that's all you can do then you're right, but if you think you can do more then you're wrong! Er, about the playing roles in one way, mind you!