I posted this basic guide awhile ago, I thought that it might help you since it gives a little bit difference insight then most how to videos address, and other guides that I've seen. For starters, I am not a high level player. I simply enjoy the game. but I do main support and I consider myself knowledgeable of the support role. I will address the game pattern itself for the role of support, and give some insight on some items which are valuable to support champs.
For a support champ a general rule is that you build a sight stone. Thats really the only general rule. You should never lock into any definite build path on a support champ. Your role in game is broken into 3 parts. part 1 is the laning phase, and your role is to disrupt the enemy adc from acquiring cs and to provide your adc with the means to win lane. This does not mean to give kills to your adc, there is a lot of misconception about that. Though generally its more beneficial for you to allow the adc to final shot enemy champs. Also during the first part, you should look to gank mid lane should the situation arise, because you're the team support, you're not the adc support. In situations where you might get a double in bot, and you have enough health you should travel up to mid to see if you can get a kill there as well. Although this isn't widely seen, a support gank gives a utility which many mid lane players aren't used to dealing with. That being said this takes practice and experience to know the appropriate time to attempt this gank.
The role you play in game post laning phase, or part 2 is that you're a second jungler. You're still not farming the jungle, but you're roaming and giving sight to the map. making sure lanes don't get pushed into you too much, and being available for battle. you should keep areas which are common battle grounds warded and sweep for enemy wards. This gives your team the ability to coordinate plans and communicate better. during this time in the game there typically arent any major team fights. but you should try to stay close to one of your allies given they may encounter an enemy or you do. In either case you have enough cc as a support to stall the fight long enough for your ally to kill them. Since you are limited to 3 wards and 1 pink you should opt to ward one jungle or the other just to provide the best possible vision. Hopefully your jungler wards the opposite jungle side, however many dont, its not your job to ward the entire map, remember that.
The third phase of the game is the end phase. This is typically when all out team fights will happen. In this current meta I believe the role of a support is to provide engages, and cc during team fights to keep your adc or carry in general alive long enough to kill the enemy team. I like items such as face of the mountain, iron locket, and randuins omen for the added shields and cc they provide in fights which are sometimes enough to keep your team alive in battle. Support items generally also double as tank items, and you can in the late game play the role as a utility tank quite well, dependent on your champion of choice.
There are sub divisions of support champs, tank supports, sustain supports, off meta supports, and "carry" supports. while the above "guide" is a basic how to play supports throughout the typical game each of these sub categories have their own unique roles.
I have provided examples of each sub category.
Tank supports: Braum, Leona, Thresh, Taric
Sustain supports: Nami, Bard, Janna, Sonna
Off Meta (poke): Vel'Koz, Brand, Veigar, Anivia
Carry supports: Annie
I didn't list every champion who plays support above, just a few to get the idea across.
If you are playing a support champion I highly suggest purchasing a support item, if nothing more then the gold income early game. If you are looking to build a support item to completion remember to build items that have good synergy with it. For example if you are playing Braum you might purchase face of the mountain, its active effect has good synergy with randuins omen over frozen heart, or for mmr it has better synergy with Locket over Banner of command. although each item has their place and unique situations when one is better than the other in game. again build for the game, do not build the same every game.
Now Zilean specifically, I don't personally play him, but I can give you some advice on him simply from me playing against him. Zilean is a fairly unique sustain poke kind of support. He has a great ability to zone off enemy adc from easy cs, and if you can land a double bomb, gives a pretty good stun. I have played against skilled zilean supports who absolutely wrecked me, and also I have played against skilled zilean supports who didn't win lane exactly, but stalled lane to a point where they won lane simply because we had to back and theyy were able to capitalize on that. Zilean with his ult, gives you the ability to go all in, or use it as an escape. He is different then all other supports, and takes some know how.
But more so then other lane roles, supports are pretty dependent on their runes and masteries. being only level 19 you suffer from that. but I hope this post was able to to help you out some.
is how mobile he is with his speed + CD reset, so try to keep an eye on mid throughout the match. If it looks like he could use some help, ping that you're on the way and hop up there. The Q-W-Q combo is enough to stun an unexpected mid-laner and then watch your mid burn him down like a moth in a flame.
and start winning the vision game. By this time (assuming you've spent a decent amount of time in lane) people will start trying to get dragon and the jungler will be hitting 6 and trying to use ultimates for ganks, so safely placing a few wards and sweeping for enemy wards will keep you and your ADC safe.