There are several buff spells she has. You summon them, and a little colored orb appears above your head. You can summon up to three buffs at a time, and then when you use the Talent Art in the middle she dismisses the summons and attacks with them in reverse order.
So there's something very important I missed at first: the buffs stop once you dismiss the spell. So if you want Agility Up, for example, you summon wind and make sure you're close enough to your teammates so they are affected by the buff. You can summon up to two more (or not), but if/when you want to attack you use the Talent Art in the middle and she will dismiss the summon, attacking the enemy. The buffs do not last as long as they are above her head, though; they stop after a while, which is noted on your Arts screen (where you manage the arts and level them up).
As you dismiss summons, her Talent Arts gauge will fill up. When it fills all the way, she will start glowing and her spells will become stronger.
My technique for using her:
1. At the start of battle, summon wind for Agility Up, which I consider most important.
2. Summon fire for strength up.
3. Summon electricity for ether up.
4. Use the spear/knee combo to topple the enemy.
5. By now, the agility buff might be close to wearing off, so I start dismissing the three buffs one by one. Agility is dismissed last, because I summoned it first.
6. Lather, rinse, repeat.
I use chain attacks to refill my summons and get some hits in. On harder enemies, I prioritize toppling the enemy whenever my arts refill.