Volibear support is one of the best ways to carry as support. He allows you to snowball your lane and be an initiator for teamfights. He has great damage without being item reliant.

Basically you need to be able to catch bottom lane. Once you catch them, spam your rotation on them. You will bring anyone down to at least half hp. As soon as the fighting starts, pop a potion to keep you healthy and fighting. You can take one hell of a beating early on. I usually wait until level 2 to be aggressive. Level 6 is a huge power spike for you. Anytime you get a kill, evaluate the situation to see if dragon is a good option before going back.

You want the lane to be pushed up to your tower so you have space to chase people. There is nothing worse than being at the enemy tower just waiting for the enemy jungler to come gank you. Ask your adc to only last hit the creeps. When creeps are in the middle of the bushes, stay in the bushes. If their support or adc gets to close, punish them. One awesome thing about voli is that you can go hard on their supports and tank the adc's damage while winning the exchange. He starts 650 hp, plus 30% heal from his passive, plus a potion ticking for 150 hp. This allows you to tank about 1000 damage before dying. Always pop a potion when the battle starts.

If you are having trouble with disengages like tristana's jump or morg's spell shield, remember that your Q is on shorter cd than their abilities. You can fake charge at them to force their ability. If they come back in lane too soon, then go HAAM when Q is back up. Usually the enemy players skill is more important than which champion they are playing. Play aggressive early on and try to get that snowball rolling. Try to force the enemies out of lane.

You get countered by a composition that can keep you from engaging them with knockbacks or dashes AND who can poke you down. They have to be able to do both otherwise you can find ways to punish them by zoning the teams without poke and engaging the teams without escapes.