I actually solo supported from silver to plat.
I've always been stuck feeling dirty with premades, as people are either my elo or below and I feel like they'd actually hold me back since I believe I'm capable of higher elo, or they're actually smurfs from a higher elo, and then I'd feel like I was getting boosted by queueing with them. As such, solo life forever.
Anyway, 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), 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.
Figure out what style suits you best, and adopt a champion or two (maybe more, but try not to be overly ambitious if your goal is only gold) to master that style with. Remember you are almost certainly not even remotely close to a peeling god/playmaking god/secret carry right now, so you should focus on yourself and try to aspire to one of those things rather than blame your teammates for their ineptitude. Once again, supports can carry games using those styles, if they're good enough, so don't try to play the victim and say you can't climb because you're a support main.
Also, remember you're the support for the team, not necessarily for the adc. ADC is your primary concern in early game of course, but if mid-late roles around and it's clear the adc is inept and the mid is a god, then feel free to cuddle up to them and be their personal peeler/play maker. The adc might grumble, but if teaming up with the mid wins the game, then so be it.
Also also, ward. Vision is your best friend. If you disagree, ward more and spend your efforts figuring out why vision is important, because it absolutely is.
