Riot Games revealed the abilities for Zeri after a prolonged period of teasing the character as she made her way to the PBE.
Zeri is a highly mobile marksman that is coming to League of Legends live servers in a couple of weeks. At the moment, she is on PBE so the numbers on her abilities may not be final. That said, it's safe to assume functionality will remain the same during the testing period and launch.
Her passive is Living Battery, which speeds the champion up each time she is shielded. When Zeri attacks a shielded enemy, she steals a portion of it.
Burst Fire is Zeri's Q ability and has both passive and active parts. The passive portion makes her auto attacks do magic damage, scale with AP and they are treated as abilities. It also makes her auto attacks and moving build up energy that will empower a single attack to slow enemies and deal more damage in a manner similar to Stormrazor.
Activating Burst Fire shoots seven rounds in quick succession to deal physical damage to the first enemy hit and her autos then flip to scaling with AD and are treated as attacks.
Zeri's W, Ultrashock Laser, will result in a line skillshot that slows and damages the first enemy hit. Shooting a wall wit hit will result in a long-range laser from the point of impact.
Spark Surge, the E ability, allows Zeri to traverse terrain with mechanics similar to Bard and Talon.
Finally, the ultimate ability is called Lightning Crash and it discharges a large AoE burst of electricity that overcharges Zeri. Overcharging grants her more damage, attack speed and movement speed. Damaging champions refreshes the overcharge duration and increases movement speed further and this doesn't appear to have a cap so far, which will likely result in some extremely fast ADCs on the Rift, especially if the other team has Jhin.
It also makes Zeri's auto attacks shoot chain lightning that can damage multiple foes.