Take Flash as your primary summoner. Flash is a crucial tool due to its assortment of offensive and defensive uses.
After patch 4.5, you have a ton of viable options for your secondary Summoner. You can choose Barrier, Heal, Cleanseor Exhaust.
Barrier and Heal serve the same purpose, damage mitigation, and thus will be your main choices.
[Barrier|CD: 3min 30sec]
Opt for Barrier vs predictable burst damage likely combo'd with ignite (assassins). Or when your support wants to take Heal.
[Heal|CD: 4min|Range: 700]
Default to Heal.
After the most recent Heal nerfs, using Heal applies a debuff that halves the effect of other Summoner Heals for 30 seconds. It's still viable to run double Heal but it's no longer so strong that it overpowers other options.
As of patch 4.6 Heal no longer removes healing debuffs.
Movement speed duration halved to 1 (4.10)
Heal decreased to 90-345 (4.13)
Despite these nerfs, Heal is still the default option.
[Cleanse|CD: 3min 30sec]
Opt for Cleanse vs hard CC. Like [Ashe], [Leona] or [Rammus].
Note: Cleanse will not work on crowd control that "suppresses" you. ([Malz] [Warwick] and [Skarner] Ults)
[Exhaust|CD 3min 30sec|Range: 650]
Opt for Exhaust for dueling potential or vs divers.