(Copy pasted from a post I made on the subject last week, speaking as someone who solo supported from silver to plat)
Theres basically 3 ways of 'carrying' as a support:
You can be a peeling god, constantly saving your teammates from themselves and preventing the enemies from getting fed until eventually your carries get lucky and pick up some kills and start snowballing (since the enemies have few to no kills). Think Janna/soraka.
You can be a play making god, basically spoonfeeding kills to your carries. Think Blitz/thresh.
You can be a damage carry yourself, trusting that your superior skill will outweigh the xp/gold disadvantage you have. Think brand/vel'koz.
The third route is unlikely to be very effective in gold or above, and probably builds bad habits. It exists (and I predict will be the most recommended route in low elo), but I don't recommend it. It'll get you out of bronze elo and maybe silver if your mechanics are good, but really you should be playing a different role if thats where your skills lie.
The playmaking route is more proactive, and probably more exciting for most people. If your carries follow up, they will get very fed, and they should be able to carry even if they aren't actually that good, simply because they're up 5+ kills. The downside is, not all carries will follow up appropriately, and in many champions cases you'll be left in a bad spot, potentially feeding the enemy team instead.
The peeling route was my primary route. It's often more reactive and arguably more boring (I enjoy it, and find it very satisfying to shut down someones all in attempt), but you can do your job without needing much cooperation, which can be useful for some of the less talented teammates you'll have. Occasionally you'll have particularly talented teammates who can almost carry on their own, and having the extra bit of peel enables them to do their thing.