Play by the click-the-path-first rule: give Zeri a long move command, fire Q inside that line, and weave charged autos into last hits or small punish windows instead of re-clicking yourself into dead stops
In bot lane, E belongs to the enemy support until the hook or stun is gone, so only spend the dash for those short Q -> charged auto -> Q punish windows after lane has shown it cannot answer them
Start R on contact with a target you can keep shooting, because Zeri gets much better as games stretch but still swings hard with early gold deficits if she never gets an overcharge window that stays alive
Start by making your next R easy to keep alive instead of trying to create a hero entry. Sit on waves you can actually collect, keep E for the spell that would force you out, and let the first target be whoever walks into your range first, even if it is not the carry. Your job is to rebuild uptime, not prove damage from a bad angle. If a fight starts with you wall-riding into fog or dashing forward before key engage is shown, you usually just lose the one tool that keeps the fight playable. Behind Zeri comes back through clean farm, charged-auto punish windows, and an ult that begins on contact.
Zeri's Attacks deal magic damage and are treated as Abilities. Moving and casting Burst Fire stores up energy in Zeri's Sparkpack. When fully charged her next Attack deals bonus damage.
Burst Fire shoots a burst of 7 rounds that deal attack damage to the first enemy hit. This Ability is treated as an Attack.
Zeri fires an electric pulse that slows and damages the first enemy hit. If the pulse hits a wall it expands into a long range laser.
Zeri dashes a short distance and energizes Burst Fire to pierce through enemies. She will vault and grind over any terrain she touches.
Zeri discharges a nova of electricity and overcharges herself, gaining increased damage and stacking Move Speed that refreshes and gets stronger every time she hits an enemy champion. While overcharged, Burst fire becomes a faster triple shot that chains lightning between enemies.