Abilities: I like maxing W first, Q second, and E last, R whenever it's up. This is more of a preferance thing. I max Q second for the super short CD and damage. If you want the long stun duration, then go for it.
Laning phase: Start with E against melee or Q against ranged.
Generally against melee, You wanna try to get the E stun - auto off when trading, then walk off before they can hit you. I usually play it safe until level 4, then I play more aggressive unless they are stronger fighters in lane, such as Renekton or Pantheon.
Generally against ranged, at level 1 stay in the back and just Q the minions to farm. When you reach around level 3-4 , Q to a low minion next to the enemy, E and auto the hell out of them, Q them to kill, if not then back off, they should be low.
When you get 6, you can basically 1v1 anybody, unless they are ahead.
Late game: Irelia does a SHIT ton of damage with just Trinity, so I would usually just build straight tank after I finish Trinity. The only problem is that you can focus on one person at a time, so you won't be as useful during team fights most of the time. So I tend to split push more often. If you need to be in a team fight, then just try to get picks on the backline, you should be tanky enough to sustain the damage and do damage at the same time.
Build: It's a new season, I have no idea, sorry bud. Im still testing out builds.