Where to Get Conjuration Training in Skyrim?

The following Quests increase the Conjuration skill: Find Pantea's Flute for Pantea Ateia in the Bards College in Solitude. This quest also increases Alteration, Enchanting, Destruction, Restoration, and Illusion.

What is the fastest way to train conjuration in Skyrim?

Conjuring up a creature and a weapon, and then entering combat does level up your conjuration skill. So, try to just conjure a creature and use a bound weapon in all fights, this will level up your conjuration skill relatively quickly.

Where is the conjuration master in Skyrim?

Phinis Gestor is a Breton conjurer at the College of Winterhold, and an expert-level trainer in Conjuration. When your conjuration skill reaches level 90, Phinis offers a quest that, when completed, rewards you with the Flame Thrall spell.