Do well, then start making calls. Your people will listen to you. At that point, focus on taking objectives as a coordinated unit. Dragon, Baron, towers, inhibs. Explain what you want your team to do in a nice way. Caution ping, warn quickly if you notice people are up, have homeguard. Encourage your support to ward. Try your best to defuse/prevent conflicts. To carry is not just to do well yourself, but to bring out the best in your teammates so that you can work as a cohesive unit.
You can't do this if you're support, only your ADC listens. In solo queue, this usually works best when you're mid or jungle, because your team comes to trust you and you build rapport easier as you help them globally through ganks and domination and success at achieving the goals you set out for the team. --- "When you want to be successful as bad as you want to breathe, then you'll be successful!"
In my opinion mid carries best in solo que; at least for me they never listen to me when I jungle no matter if I am making incredible plays and carrying our team hard. Mid is easiest because I don't have to depend on anyone really and therefore normally always go positive and get fed. I noticed though as ADC seems like I carry the least which is hysterical. --- Sometimes you get the coal mine, and sometimes you get the shaft.