Yo as a fellow support player who hit Gold with relative ease after putting in some work let me offer what I can.
So first of all know that right now support sucks, just because of the 4 man bot tower dives. I am actually just not playing as support right now because that right there can change a game and I prefer to be mid where I can get our team to be the one that 4 man dives.
That being said I will give what advice I can.
Keep in mind I tend to play hook supports when climbing as well as a good amount of Taric, some Raka, and the occasional other support by request.
Some general tips I can give before I get into more mechanical things:
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In champ select be friendly, ask people how their day is going etc.
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Ask your ADC if they have any support pref and try to fill in the areas your team is lacking in
(A team must have Waveclear (Not gonna be your job usually) Engage (You can offer) and Damage (You can offer))
Beyond that you can be peel, engage, tank, poke, etc. Just try to fit your team comp.
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If someone is being salty mute them. Don't argue with them. Don't try to cheer them up. Mute them.
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Placements don't matter. As you win your MMR goes up. When you lose it goes down. All you care about is raising that. In the end placements don't matter so long as you play enough.
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Sometimes your teamates will do crap. There are two ways to play LoL. The worker ant and the leader. If you are a leader you lead. You don't ask your team to let you lead, you just do it. Sometimes they wont follow, and that is fine. On to the next game. The other way to play (and the way I play) is the worker ant. Here you do your job. You assume your teammates will also do their job. Sometimes they wont. Sometimes they will wander off a cliff. That is fine. Just keep doing your job. Eventually you will play with worker ants who don't get lost and you will win, because winning is all that matters.
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Surrendering. In general I go with the never surrender so long as you can see an opening. Does you team scale better? Hang in. However if your team is far down, they want to surrender, and you aren't going to outscale it is better to move on to the next game as quickly as possible.
Things you can do to help allies:
An ally died and their laner is staying? Time your roam to gank as they get back. Call in your jungler too if you get the chance.
Someone is just getting wrecked? If it is top try and get your ADC to swap top with you. The two of you can take on one enemy more easily and your TOP will be less likely to get into dangerous positions in a 2v1.
The support might even roam up to match instead of both their lanes swapping, which means their ADC is a sitting duck for your jungler.
Mid is a bit trickier to lane swap with but you can roam to them a lot more than you can to top.
Mechanics aka LCS BIG PLAYS
Now since you mentioned you play most champions I can't give specifics but remember that if you KNOW you can burn a carries flash by burning yours do it. Supports generally grab the mastery that gives shorter Summoner CDs and an immobile ADC or Mage missing flash is more important than a Nami or something.
Just remember to build for your team/enemy team.
Watch the map, you have more time for this than anyone but the jungler. Map awareness is key to rising.
If you give me a couple supports you want specific tips on I will see what I can do.
Lastly, and most importantly just remember. So long as you win 51/101 games you will rise. There is an element of luck, mechanics, game knowledge, and social skills that are all required to rise in the rankings decently. The more of one you have the less of another you need, but they are all important. Sometimes a teammate is going to feed, sometimes they will carry, sometimes they will troll. Not much you can do about that. But remember: There are 5 players on the enemy team that could feed or troll or afk. You can't control that. However so long as you never do those things there are only 4 players on your team that can feed troll or afk. That is the key to rising, to not stoop to their level or be put off when it happens.
Just do you job, play games, and you will slowly rise.