Kaeya

4★

CryoSwordOff-field Damage

TL;DR

Kaeya's Burst leaves three icicles spinning around whoever is on the field, and they keep hitting things with Cryo for about 8 seconds after he's gone. His Skill is a cheap Cryo blast on a 6 second cooldown that hands out energy particles. So: Skill, Burst, swap out, let somebody else do the killing while his ice keeps landing.

Rotation

Press Skill (E) for the Cryo blast and the particles.
Press Burst (Q) to spawn the icicles.
Swap to your damage dealer. The icicles follow them, not Kaeya.
Come back for another Skill (E) when it's up, roughly every 6 seconds if you have the time.

Abilities

Skill (E)	A cone of ice in front of him. About a 6 second cooldown, which is short enough to press twice in a rotation. It also heals him a little on every hit, so he tends to look after himself.
Burst (Q)	Three icicles orbit the active character for about 8 seconds, hitting whatever they pass through. Costs 60 Energy, 15 second cooldown. This is the part that works while he's off the field.

What actually matters

The two or three real decisions. Everything else is noise.

The icicles go where your carry goes. They latch onto whoever is on the field, so you get Cryo on the enemy without Kaeya standing there. Burst, then leave.
Freeze things and he pays you in particles. One of his passives makes enemies his Skill freezes cough up to two extra energy particles. Bring water, freeze the enemy, and your Cryo carry stops running out of Energy.
Energy Recharge, enough to burst every rotation. 60 Energy is not much and his Skill is generous, so somewhere around 130% is usually fine. He isn't the character to pour Energy Recharge into.

Gear

A build that works. KeqingMains lists every other option.

Weapon	Energy Recharge with some attack behind it. Favonius Sword, since its passive throws out more particles and particles are half of what he's for.
Artifacts	4-piece Noblesse Oblige. His burst is the thing he's on the field to press, and it hands the party 20% attack every time.
Main stats	Energy Recharge sands, Cryo goblet, Crit Rate circlet. If you're only using him for the Cryo and the particles, don't lose sleep over the circlet.

Works well with

Hydro

Pyro

Hydro on the team freezes things, which is where his particle passive pays off. Pyro melts instead, which trades the crowd control for bigger numbers.

Don't bother

Playing him on the field. His normal attacks are fine and completely unremarkable, and standing there costs your real carry time.
Waiting on his burst cooldown. It's 15 seconds and his Skill is 6, so press E again rather than standing around.
His C4 shield. It only fires when he drops under 20% health, which mostly means he was about to die.
Counting on the icicles to hit a small or moving target. They orbit, so they miss plenty. Cryo lands often enough anyway.

Want the full theorycrafting version? Read Kaeya on KeqingMains.