Solo queue and our team needs support; lock in Sona. Go to lane, AD carry turret dives 60% health Sion and Taric. Complains to Sona for not supporting well enough. Game goes on and AD carry continues to make terrible decisions and complains about support. What should a support character do in this sort of situation?
This is a tough question to answer because you aren't in control of the other person's actions. Generally speaking, it's far easier to support more passive gameplay, and the difficulty of supporting increases as the carry becomes more aggressive. Ultimately, like in the situation you present, supporting becomes impossible in any meaningful manner. The way I see it, you have three options:
You can voice your concerns to them and see if you can get them to be less aggressive, which makes supporting them easier (or possible)
You can accept that they're going to be very aggressive and tune your play to match as best you can.
If things are truly hopeless, you can switch to a more roaming role and try to help other lanes win their matchups. Careful about stealing experience, but with Sona's ultimate and some well-placed heals (for instance), you can be a force for good for the rest of the team.
The first option is the one you should pursue first. The relationship between AD Carry and Support needs to be tight-knit for success. Often, even aggressive AD carries realize this. The second option is what you'll be doing a lot. You have a duty to your carry to support them (hence the name of the role). Try not to die, obviously, but do everything else in your power to help them accomplish whatever they're trying to do. The third option should be an absolute last resort. Just giving up on your lane isn't something to be done lightly.
If the AD carry is aggressive you should be prepared to ward the river for ganks, and force trades too if possible. If he's being overly retardet and just impossible to co-operate with, hit up the fancy ignore button.
What if the support is bad? I'm a decent AD player and I sometimes get way too passive supports. For example, i was playing corki and had a Leona supporting me who should be an aggressive laner who forces trades and keeps the opposing carry in fear of the pull-stun combo, but instead she just literally AFK'd at our bush.
They had Graves & Blitzcrank combo which was hella aggressive, so i was forced to play passively because 2v1 was not an option. Once blitz caught me off guard with his pull, i was able to valkyrie away and stay alive with heal, but right afterwards the leona decides to go in 2v1 while i had literally 100 hp left? and dies right off the bat, giving the graves 1-0 lead. From then on the lane just snowballed to their favour making us lose the lane and i got all the blames from it from the team. ''Nice feed corki'' etc
So its not just the AD carry who needs to be good, its also the support. When i do get a good support i usually end up with a 12-4, 8-2 17-4 ~~ ish score on any AD.
There is not not much you can do. The support role is about supporting good carries; if the carry is bad, support during the lane phase can only help so much.