Spellthief's Edge is the standard gold income item for most AP supports. It boosts every stat you need and is very easy to keep up your procs with auto attacks and two for ones with Ebb and Flow. The Total Biscuit of Rejuvenation help sustain your health and mana, keeping you in lane longer. The Warding Totem is the standard trinket for all supports until they get their Sightstone.
The Ionian Boots of Lucidity are necessary because you want to reach the 45% cooldown reduction so you can cast your spells as much as possible in the late game. Rylai's Crystal Scepter gives you a huge chunk of health and ability power, along with a powerful slow on all of your abilities; adding to your already insane amount of crowd control. Eye of the Watchers is your primary vision tool, the reason you build into this instead of Frost Queen's Claim is to free up an inventory slot for more powerful items later on. Oracle Alteration is for reducing enemy vision control throughout the game.
If you are doing very well early on or feel extremely confident about your laning phase, it is a good idea to purchase The Dark Seal. It's affordable and the stats you gain if you stack it up make it an extremely gold efficient item, helping you take your lead even further. The low cost of it means that if you don't end up doing well you can always sell it later on and not lose a huge amount of gold.
Sometimes you might find that your team needs a little boost in the damage department. Luden's Echo is that little boost you can provide. The massive AP bonus synergizes well with you kit, and the AOE ability proc's the slow from Rylai's Crystal Scepter.
The game is 50 minutes in and everyone in the game has their full builds, you're drowning in gold with nothing to spend it on. This is the point where you wanna sell one of your support items and slap on the death hat. The AP bonus it provides to your healing, along with the pure damage you get will more than make up for losing a support item.
This is an item you want to pick up if you end up against too much crowd control. If your carries can't move then you can't win. Good champs to pick this up against are initiators like Maokai, Nautilus, or Sejuani. It's also sometimes good to grab it when you're against a bot lane that can chain CC for easy kills, such as Ashe and Zyra.
Redemption is the more defensive pick of the big two support items. You pick this when you need a strong stream of healing for your entire team. The added health makes you more durable and the passive boosts your healing. But what is most important about this item is the incredibly strong active. The AOE heal / damage effects a large area and has a huge cast range, as well as having the ability to be cast while you are dead.
When you have at least two champs on your team that rely on auto attacks this item is golden. The healing buff it gives to you, as well as the on hit damage and on hit healing it gives to people you heal make it synergize extremely well with Ebb and Flow. That, along with passive stats you get from this make it very strong.