Xayah is a unique ability-focused marksman that has intense waveclear and CC that allows her to play mindgames with her opponent and control space.
For runes, the best keystone for Xayah is probably Lethal Tempo. More attack speed means more damage and more feathers. Triumph, Legend: Bloodline, and Coup De Grace with Sorcery secondary for Absolute Focus and Gathering Storm is a good rune page for Xayah.
For items, you need attack speed and crit. Generally, you're gonna build a B.F. Sword upgrade for your first item, then follow it up with a Zeal upgrade, followed by Infinity Edge, followed by a defensive item. Personally, I really love
on Xayah. The extra CDR and mana sustain let you spam out your spells and feathers, and Essence Flare really kicks things into overdrive.
is usually the safer pick. A good go-to build path would be:

For your abilities, you want to max Bladecaller (E) first, followed by Deadly Plumage (W), and max Double Daggers (Q) last. It may seem tempting to max Q first since it seems like your damage ability, but stop. It's main purpose is to poke, get feathers on the ground, and trigger your passive. Bladecaller is your bread and butter damage ability. Max it first.
Your main combo will be to use Q to drop two feathers on somebody, throw an auto at them, and immediately recall those three feathers with your E to root the target in place. This combo is great for catching people out, for easy trades, or setting up follow-up damage and CC from your support.
Your W is a damage and attack speed steroid that gives you movement speed while fighting champions. It has a long cooldown, so be sure to use it only when you're committing to dealing damage. It's also amazing for pushing down towers and getting that sweet, sweet turret plating.
As for her ult, I'm going to say this as clearly as I possibly can: FEATHERSTORM IS A DEFENSIVE ULTIMATE. Its primary purpose is to avoid damage and CC. You are squishy and have no mobility. Believe me, the temptation to go gung-ho and use it to root somebody and initiate a fight for the team is great, but doing this will get you killed. You are still a marksman. If you see an opportunity that guarantees a kill with it, go for it, but generally you want to hang onto it to avoid something that will get you killed and use the damage and feathers on the ground to snare the person who tried to kill you while you run away.