From the wiki, for her ultimate.
MAXIMUM PHYSICAL DAMAGE TO ONE TARGET: 320 / 480 / 640 (+ 200% AP) (+ 240% bonus AD)
Of this, your heal 25% of the damage deals to champions and 10% of the damage dealt to minions. While this damage can fall off later in the game against more durable champions (since you don't usually build armor pen), it can deal a lot of damage to squishy champions, who are the ones you want to focus. It's also on a low cooldown (70/60/50) so it can be used to trade or waveclear as desired.
However, the main appeal of her ultimate is that it can give you up to 4 procs of Spellblade from Sheen, which is a significant amount of damage, and a burst of health during a fight.
For build recommendations, I would suggest looking at videos by CarryMe2Plat since he's a high-tier Irelia main. For a basic build, I would recommend:
- 21/9/0 Masteries
- AD Marks and Quints, Armor Seals, MR Glyphs.
-Health Regen, Attack Speed, Movespeed, Armor, or MR quints are also good options.
- Ninja Tabi or Mercury Treads, Trinity Force, Frozen Heart, Spirit Visage, Blade of the Ruined King, Randuin's Omen
- Skill Order: QEWEWR against Ranged Champions, EQWEWR against melee champions, R>W>E>Q
- Summoner Spells: Teleport or Ignite, Flash
Trinity Force is your core item, since Irelia synergizes extremely well with it. I would recommend rushing it in most matchups, maybe purchasing a mid-tier defensive item or defensive boots beforehand if necessary. Phage is your general damage and durability item and Sheen is better when you are ahead and want the damage to snowball. I would recommend getting Zeal as the last component in most cases.
If you need to use Q to initiate trades, try Qing to a low health minion beside them so that the cooldown is reset. When your W duration is almost over, you can Q-AA the enemy one last time for additional damage and a sheen proc. Q applies on-hit effects (Sheen and W) and I believe Q also functions as an autoattack reset, so keep that in mind.
For starting items, I would recommend taking ClothArmor+5HP or CrystallineFlask+4HP while you are learning her. She's a bit on the weak side early game but scales well into the mid and late game after you finish Trinity Force. Teleport is useful in lane since it helps you mitigate mistakes and gives you more pressure on the map, and help you survive your weakish early game. Irelia really starts to pick up once she has W maxed and has a Sheen, so be aware of that.