Early Game
As what most solotop players aim to do, you should just farm like a boss. If harrassing the opponent means losing some farms, get the farms. You shine a lot better mid-late game. At lvl 3/4 for you should have all three of your spells, 6 for you will have your utlimate, and 9 for your Hiten Style will be maxed out.

You should be invading the enemy jungle or taking your own, if you lane is too pushed.



Mid Game
During this time, your power starts to shine. You will deal loads of damage. At about 20 minutes try to have at least 100 farms. I see no reason why you can't have 100. If you are good, you should have at least 180. A good way to keep track of how many minions kills is good, is by how many minutes in game X10. This is quite hard to achieve though.

By this time, you should have also finished your Trinity Force or your Wit's End+ Phage, depending on what build you chose to use.

Generally if you know how to farm and know how to play Irelia, you should be picking up some kills and assists here and there. Even if you weren't, your farm amount should make up for that.



Late Game
If the enemy is quite tanky now, you will notice you are not as strong as the mid game phase, however, don't be discouraged. With most of your items, you should still do loads of damage and also tank very well.

You should be one of the people that initiate teamfights, waiting for the right chances, and making the right calls and not throwing the game in return. Jump on their AD or AP carry in teamfights, and win. Sometimes damaging them enough to scare them out of the teamfight is enough; use your best judgement.

Pros


+ Awesome solo toper
+ Easy to farm with
+ Unstoppable with items
+ Great sustain
+ Kills carries
+ Fun to play



Cons

- Item dependent
- Squishy without runes or masteries
- Needs to farm well
- Not good against tanky people
- Melee champion
- Receives nerfs on an average basis