http://images.wikia.com/leagueoflegends/images/1/14/Irelia.jpg
The Image is not from me but I like it and because of that I took it in here. :)

Hey Guys and Girls, this is my first Guide on Mobafire and i hope you will be nice to me :).
Im from Germany so my English is not the best but i hope you´ll understand me^^.

Why i play/like Irelia
I like Irelia because she is very strong in Early-, Mid- AND Lategame.
Also she is very useful in Teamfights and not really hard to master.
In my opinion she is the Queen of solotop, and noone can stop her if she is well played.

Pros: Very tanky Cons:Very item dependant
Does thuogh very much DMG does not too much DMG early game(she does nice
Has the best skill combo DMG but not
has heal in her spells too much:( )
can deal true DMG needs VERY much farm.
Great farming with Q.

I take those Runes on her because she needs to be played tanky AND with DMG, but the DMG comes later.
The defensive Runes will give you a nice push of you´re Resistances and life, and the pen.-runes will help you to do Nice DMG in early-, mid- and lategame.

I go 0-26-4 with Irelia because its better to play her more Defensive. The DMG comes by itself if you have you´re Warmorg´s Armor + Atma´s Impaler + Wit´s End.

Boots
I pick Mercs, because of the Tenacity. It helps you pretty much and with you´re passive you cant be stunned very long and escape from nearly every situation.
Other Items
I think these Items are the right choice on Irelia because they push you´re live, they push you´re Resistances and the most important one- they push you´re DMG HARDCORE. No im not exaggerating, you´re auto attacks + you´re W will deal too much DMG to the enemies. Thats nearly OP^^.

The priority is R>W>Q>E. Why? Because you´re R can be casted very often and deals very nice DMG+ it heals you.(!!!!) W is the next i the list, because of the extra true DMG and heal. 3. is Q because its you´re main lasthitting skill and with the Trinity Force it deals pretty much DMG too. The last one is E, because the DMG is´nt very high and the stun or slow dont increases very much.

I think Teleport and Ghost are the right choices for a solotop like irelia, because they are the perfect skills to be by you´re team when a fight starts, or to be in lane before the enemy can push it.

The most irelia players think its cool to only farm with Q, but thats not good! take only the last hits wich you cant take with you´re auto attack with you´re Q. THATS IMPORTANT!! OTHERWISE YOU WASTE YOU´RE MANA!!!

That was my Irelia Guide and i hope that i can help you with it :) .