These are the highest DPS Runes you can get while not losing alot of AD here is my mathematical proof:

Flat AD Page: 42 DPS W/ Hiten 1
Atk Spd reds Arm Pen quints Page: 48 DPS w/ Hiten 1
Arm Pen Page: 41 DPS w/ Hiten 1
Arm Pen reds AD quints Page: 44 DPS w/ Hiten 1
Atk Spd reds AD quints Page: 49 DPS w/ Hiten 1

Note that due to diminishing returns Arm Pen runes pen less % reduction the higher the % is. Due to this AD runes are usually preferred over any other rune.

Now; Attack Speed does some pretty good stuff for Irelia. First the best, 15% more true damage for activating your Hiten Style. Along with this is 15% more healing from Hiten style since it heals for flat amounts. It also alows you to cs faster. Also 15% more AD but AD reds would increase damage by about 17%. But look at what attack speed does for you again. 15% more true damage and healing > 2% more basic attack damage.

The Armor yellows should not be changed. Magic resist can be flat or per level, whatever you prefer. AD quints gives you csing power equal to arm pen reds and ad quints. You can use Armor Pen or even Attack Speed for even more true damage and healing, but I prefer AD.

If you are winning the lane and the enemy jungler is on the other side of the map you can farm between the enemies 2 active turrets guaranteeing 100% farm and 100% damage to the enemy turret by minions instead of them hitting other minions. If the enemy tries to stop you, you could destroy them.

Irelia can use any masteries. Before season 2 masteries 15/15/0 was my favorite. It still works pretty well but due to the current nature of solo top 9/21/0 or 0/21/9 is recommended. You can also go 1/8/21.

Probably the best summoner spells for irelia are Flash and either ignite or teleport. More advanced players will use teleport for the map and dragon control and split pushing. If you are newer to irelia the ignite will help you finish off other people. Thats about it. If you need to you can always take exhaust or heal but thats about all the good SS's for irelia.

After logic and calculation Philo is better than HoG and Brutalizer is better than Phage. This is a pretty standard build besides the brutalizer and dorans shield. When in lane for around 3 minutes Doran's shield out does cloth and 5. Other alternative starting items are Regrowth Pendant and boots with 3/4 health pots. (you obtain 4 by waiting on the pad after minions spawn until you can buy the 4th potion) Also if ap is scary you can replace brutalizer or sheen with Wit's End for extra True Damage shredding.