This build isn't meant to compensate for a lack of skill. It'll help if you're already familiar with Irelia and know the mechanics. While I realize there may be better builds, this is one that I have found to work very well. You'll end up with ~230 armor and ~180 MR, which will allow your randuin's active to slow MS and AS by 35% for 6 seconds, which in team fights is amazing against right click to win champs such as Xin, Tryn, Yi, Noct, etc. If you've got any opinions on this build, feel free to share.

Marks/quints: The typical metagame in 3s results in the carry going up top. Quite often a Tryn or Xin will go up top, but just as often you'll go up against a Vayne, LeBlanc, ETC., at which point you chuckle because you have more armor penetration than they have armor. This means that for the first few levels of the game you're basically doing true damage, which helps a lot more than you may think.
Seals: Speedy Irelia is a happy Irelia. If you dive into some minions and start chasing the enemy champ, these dodge seals with the Evasion mastery and Swiftness will allow you to move a lot faster and catch up to them. The runes and masteries give you ~8.8% dodge, and if you dodge a minion you get another 10% move speed which will help you catch up a lot faster
Glyphs: Flat MR glyphs help out a lot early game, especially if you're up against an AP carry. With Irelia, you just need to survive until level 6 and dominate, and the early MR helps out a lot.

As with every Irelia build, 21 in utility is pretty standard. The bonus EXP, gold/10, mana/hp regen, move speed, and CDR is really helpful. The points in defense are pretty basic as well, and since 9 points in defense helps more than 9 in offense, its really just a matter of if you want dodge/speed, or MR/Hp regen.

I don't know why, but I rarely see a gunblade in Irelia builds. After the nerf to her ult, healing only 10% against minions, I expected spell vamp to really take off. The gunblade offers some AP to help with your E and R, attack damage thats always welcome, life steal/spell vamp for more survivability, and the active is amazing early game. Even late game, you can perma slow for over 10 seconds with E, gunblade, randuin's, E, and exhaust if necessary. This in combo with your max active Hiten Style will make anyone who gets in your line of sight seriously regret it.
I get sheen early for the passive, but I find rushing Trinity just for another 50% damage is a waste of gold early game (sheen -> trinity is the same cost as a GA/FoN, and I don't see why a trinity is that much better).
Save Sorc Shoes, just about every kind of boot is helpful for Irelia under the right circumstances, which is why I didn't include any in the item build. Against a lot of DPS champs, ninja tabi is an easy choice. It also synergizes well with your seals and masteries. Merc treads are good against casters and hard CC (merc treads + your full passive will make a 2 second stun 0/5 seconds). If they don'T have a lot of CC and you're ganking more, boots of swiftness/mobility are viable choices. Just use your own discretion.
GA is the last item I get before trinity because if you don't have a lot of armor/MR, GA really just prolongs the inevitable. At the end of this build, that 750 HP will count for a lot more with 230+ armor and ~180 MR.

To be honest, after the recent patch making Q 60/65/70/75/80 mana instead of 70, I see no reason to max it first. E offers more damage/level, as well as an increase in stun/slow duration. W offers more survivability and the active works with Bladesurge so if you land Q and 1 auto attack, thats still more damage than if you had levelled Q.
I've found that a really good burst with Irelia is E (hopefully stun), W+AA, then right after the auto attack Q for another hit of W, which is immediately followed by another AA. This is seriously deadly early game, especially if you stun them with E.

Because you're always facing a carry, exhaust is pretty much necessary. Engage them, wait will you have less % Hp than them, stun them, and then exhaust. This combo can seriously change the tides of any battle, and if you can do it early game you'll get a serious advantage over the other carry.
Flash is another useful spell for solo laning, as in the event of a gank you can flash over a wall as long as you aren't hard CC'd. Personally I prefer flash over ghost, but I suppose its personal preference.
Teleport usually replaces flash for me in 5s, as it helps a lot when solo laning as well as ganking.
Your second spell is usually up to personal preference, but I rarely play without exhaust as a solo laner. If you can manage to get a tryn to overcommit to a fight at level 1, then stun and exhaust, you're at a HUGE advantage.

This build isn't meant to compensate for a lack of skill. It'll help if you're already familiar with Irelia and know the mechanics. While I realize there may be better builds, this is one that I have found to work very well. You'll end up with ~230 armor and ~180 MR, which will allow your randuin's active to slow MS and AS by 35% for 6 seconds, which in team fights is amazing against right click to win champs such as Xin, Tryn, Yi, Noct, etc. If you've got any opinions on this build, feel free to share.