At lower levels, Final Fantasy 14: A Realm Reborn only has one healing class. This means that the Conjurer is high in demand for dungeon runs below level 30 (when Scholar becomes available). Unlike Final Fantasy 11, playing a healing class doesn't mean you have no offensive power. For the first 15 levels, before you really start grouping with other players, Conjurer can hold its own.
As a Conjurer, you get Stone right at the beginning of the game. It's not until level 2 that you learn Cure, your first healing spell, then at level 4 you learn Aero, a damage over time (DoT) spell. When you learn the Cleric Stance ability at level 6, that's when things really start to get interesting. Cleric Stance switches your mind (healing potency) and intelligence (magic damage) stats, while increasing magic damage by 10 percent lowering healing potency by 20 percent.
What Cleric Stance does is make all of your offensive spells far more damaging, while cutting how much you can heal with each Cure spell. While soloing, or any time you don't need to be steadily healing, you should always have Cleric Stance active. The combination of Stone (which causes the effect of Heavy on an enemy), Aero, Cleric Stance and Cure, the Conjurer is one of the best solo classes in the game at early levels.
The best rotation to use while soloing to level 15 is to activate Cleric Stance, then stand at maximum casting range and start a battle with Stone. This causes Heavy, which drastically slows an enemy's movement speed. As they slowly make their way to you, use Aero, which is an instant cast and DoTs the enemy, then continue to pummel the foe with Stone spells until it's dead. Use a Cure spell if you hit roughly half life, but don't worry about removing Cleric Stance. Even with the potency cut, one or two Cure spells is more than enough to get yourself back to full HP.
By the time you reach level 15, you have gained Protect (level 8) to raise the physical defense of you and any surrounding party members, Medica (level 10), which is an area of effect (AoE) version of Cure, Raise (level 12) to bring someone back to life once they've died, and Fluid Aura (level 15). In early dungeons, Fluid Aura is one of your best tools. It knocks an enemy far away from the Conjurer, and Binds it in place for six seconds. This is best used when a tank loses hate to the Conjurer and you need to get an enemy off of you.
At level 18, Conjurer learns Esuna. This removes most status ailments from yourself and party members. Early on it's primarily used to remove poison, but there are a few other status ailments here and there. At level 26, Conjurer learns Repose, which is a sleep spell. This comes in handy when there's no Thaumaturge or Black Mage in the party. If you're fighting multiple enemies at once, most tanks will appreciate the Conjurer using Repose on the extra enemies. To maximize your damage, hit each enemy with Aero before casting Repose. With this, enemies will take damage while they sleep.
Once you reach level 30 and make the transition to a White Mage, there isn't much that really changes. You learn Cure II at level 30, which is a far more powerful healing spell, but also generates more enmity and costs more MP. It's best used when a tank is getting hit with excessive damage. At level 32 you learn the trait Freecure. With this, every time you cast Cure, there's a 15 percent chance your next Cure II cast will not use any MP. As long as your tank remains above 50 percent health, use Cure to heal him until Freecure procs, then use Cure II.
The main tools that you gain between level 30 and 50 are Presence of Mind (level 30), Stoneskin (level 34), Regen (level 35), Shroud of Saints (level 38), Divine Seal (level 40), Medica II (level 50), and Benediction (level 50). Stoneskin absorbs damage equally 10 percent of the target party member's total HP, which is bumped to 18 percent with the Graniteskin trait learned at level 36. This should be cast at the beginning of every dungeon, alongside Protect. It's best to also make sure the tank has Stoneskin at the end of every battle to prepare him for the next fight. If you can keep it on all of the party members, that's great, but the tank takes priority.
When you learn Regen, this should always be cast on a tank right after he engages an enemy. Do not cast it beforehand, or you may take the hate from the tank. It also works well when a party member has taken small damage, but is not in need of an immediate cure. This is doubled up at level 50 when you gain Medica II, which is an AoE spell like Medica, but in addition to healing, it adds the effect of Regen. The Regen with Medica II isn't as potent as the standalone Regen spell, but the two stack (as well as stacking with other White Mage Medica II and Regen casts) to create a very powerful regen effect.
Benediction is basically your emergency healing spell. It can only be used once every five minutes (300 seconds), but it instant restores all of the target's HP. This should only be used if the tank or another party member is about to die. You generally want to save it for the tank, but if you're not fighting a boss anytime soon, it can be used to save another party member if need be.
Presence of Mind, Shroud of Saints and Divine Seal are all more situational than a White Mage's other spells and abilities. Presence of Mind increases your casting speed for 10 seconds, Divine Seal increases your healing potency by 30 percent for 15 seconds and Shroud of Saints cuts your enmity in half, but more importantly, it gives you the effect of Refresh for 15 seconds.
Shroud of Saints should be used any time your MP drops by 20 percent or more. The recast on it is only three minutes, and it can come in handy during long fights. Presence of Mind has a five minute recast timer and should generally be used during boss battles, but Divine Seal can be cast once a minute and should be used any time you're having trouble keeping up with healing.