Tartaglia

5★

HydroBowMain Damage

TL;DR

Tartaglia's Skill throws away the bow and hands him water blades for up to 30 seconds. In that stance his attacks are Hydro. Hitting an enemy carrying his mark sets off an extra explosion. The catch is the cooldown, which grows the longer you stay in melee. Ten seconds in, Burst, get out.

Rotation

Skill (E) to go into melee. His attacks turn Hydro immediately.
Normal Attack for around 10 seconds. His crits put the mark on things. Every hit on a marked enemy sets off a Hydro explosion.
Burst (Q) while still in melee, which clears the marks and blows each one up.
Skill (E) again to step out of melee on your own terms, then swap off.
Let the rest of the team fight while the cooldown runs down.

Abilities

Skill (E)	Swaps him to water blades for up to 30 seconds. Normal and Charged Attacks become Hydro that nothing can override. Pressing it again ends the stance early. The cooldown depends on how long he stayed: as little as 6 seconds for a quick trip, up to 45 if you let it time out on its own.
His mark	Lasts 18 seconds on an enemy. Hitting a marked enemy in melee sets off an area Hydro explosion, once every 1.5 seconds. Killing a marked enemy spreads the mark to everything nearby.
Burst (Q)	60 Energy, back in 15 seconds. Cast in melee it's a wide slash that strips the marks off every enemy hit and detonates each one. Cast with the bow out it's a single arrow that marks the target and refunds some of its own Energy.
Charged Attack	With the bow out, a fully charged shot applies the mark. That's the only reason to use it, though mostly you won't.

The one mechanic to understand

The cooldown is the price of the stance.

Melee is where all his damage lives, so the whole character is a question of how long you stay in it. Come out after about 10 seconds and the cooldown is manageable, so he's back for the next rotation. Ride the full 30 seconds and let the game drag him out and you're looking at 45 seconds of bow. Press the Skill again to leave rather than waiting for the timer, which keeps the shorter penalty.

What actually matters

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

Crit Rate, because the marks come from crits. In melee his crits apply the mark, so a low Crit build applies it patchily and misses the explosions that follow.
Level his Normal Attacks first. The explosions count as Normal Attack damage, so that one talent covers both halves of his kit.
Energy Recharge, moderately. The Burst is 60 and the melee explosions feed him particles, so roughly 130% is enough to get it every rotation.
He applies Hydro constantly. A lot of what he's worth is soaking the enemy for a Pyro or Electro teammate rather than his own numbers.

Gear

A build that works. KeqingMains lists every other option.

Weapon	Crit and Attack, plus anything that boosts Normal Attacks. Rust is a standard banner 4-star that adds 40% Normal Attack damage. Its Charged Attack penalty costs him nothing.
Artifacts	4-piece Heart of Depth. Hydro damage on the two-piece, then 30% Normal Attack damage for 15 seconds after his Skill, which is the exact window he's in melee for.
Main stats	Attack sands, Hydro damage goblet, Crit circlet.

Works well with

Pyro

Electro

Pyro is the big one, since a soaked enemy takes roughly double from fire. Electro works on the same logic. He's also happy to be the Hydro in somebody else's team and never touch melee at all.

Don't bother

Sitting in melee for the full 30 seconds. The cooldown makes you pay for every extra second.
Aimed shots as a damage plan. They're there to apply the mark when he's out of melee.
Elemental Mastery. His teammates trigger the reactions, not him.
Plunging attacks in melee. The stance removes them.

Want the full theorycrafting version? Read Tartaglia on KeqingMains.