Well guys, this is my very first guide on MOBAfire so give me a little lee-way on keeping the guide up-to-date and getting used to the structure of making guides but I promise you this guide is WORTH reading. Also, thank you to Minami for showing me to a decent beginner guide so I can improve on this guide and any other guide I create. Also, I gotta give a shout out to JhoiJhoi for making her epic beginner's guide (that can be found here). By the way, don't forget to always comment on the guide and critique on my handy work so in the future, I can make my guides that much better for you guys. Thanks! (Also, hit me up anytime on-line: Summ. Name - LoG Jasper)

Let's start off with the reasons for and against using Irelia solo top and in general.

Pros

Amazing at trading against almost any champion
Insane sustain in lane
High mobility
Built-in ease of farming
Has a decent amount of CC
Sets up ganks very nicely
Late game is CRAZY if beginning game goes well
Aviator skin is sooo sexy (My opinion)

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Cons

The people she can't trade with utterly shut her down
Very mana hungry and kind of longish cooldowns
Timing with farming mechanism is crucial
Beginning game is pretty weak
To do well late game, beginning game has to be excellent
Sustain just recently got nerfed (Still insane though)
No legendary skin yet

For your Runes...

Marks

Greater Mark of Attack Speed for your Hiten Style to give the health regen per auto attack more frequently
greater mark of desolation so your opponent's armor gets nullified

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Seals

Greater Seal of Armor so your AD opponents do less damage to you

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Glyphs

Greater Glyph of Scaling Magic Resist so your AP opponents do less damage to you
Greater Glyph of Cooldown Reduction so you can farm with your Bladesurge easier and so you can use your Transcendent Blades more frequently

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Quintessence

greater quintessence of desolation so your opponent's armor gets nullified (Or if you think that the armor penetration is pointless in Quintessences, you can always go with Greater Quintessence of Attack Damage so your auto attacks and abilities do even more damage)

For your Masteries...
9/21/0 gives enough damage to be useful for laning but also balances for more tankiness so you can make use of your passive and tank all of the enemy's CC and initial burst damage. Easy enough.

For your Items...
Self-explanitory. One is for a majorily AP or CC team and the other is for a heavy AD auto attack team. Now, for the last item, you don't always have to go Warmog's Armor depending on your situation...
Personally, I go Warmog's Armor the extra health because armor / magic resist is nothing without health
An Infinity Edge is also a viable choice to go with your Trinity Force because it adds to how much damage you do with your abilities and it also increases your critical strikes and the chance of them happening and who wouldn't want that?
Banshee's Veil is nice against fed casters such as Ryze or Ahri for the spell block and also gives bonus health and mana for extra tankiness
And there's always the oh-so pleasant Atma's Impaler for the added armor and the extra damage from your health

For your Skills...
Simple and easy. First 3 levels are obviously the 3 skills. Now, there is a little change up you can do:
Instead of maxing Equilibrium Strike first, you can always max your Hiten Style first if you need the extra sustain early in lane
If you do end up maxing Hiten Style first instead, just switch the Hiten Style and Equilibrium Strike leveling orders in the table
I honestly like to max my Equilibrium Strike first though for the amazing ganking opportunities it offers but it's completely up to you

For you Summoner Spells...
Ghost and Teleport are my favorite spells for ANY solo top.
Ghost gives an insane movement speed increase for chasing down enemies
Teleport for teleporting to wards and such for teamfights or getting to a lane quickly
Some skills that MIGHT* be acceptable but I still think aren't needed...
Flashclears a decent amount of land getting in and out of fights but Ghost travels over SO much more distance and with her Bladesurge blink, there's no need for Flash initiate
Ignite is good for "sealing the deal" in fights but with her Bladesurge Equilibrium Strike Transcendent Blades combo, it's just not useful
Some people might say Heal but you already have a **** ton of sustain from your Hiten Style and Transcendent Blades so there's no point for it
Exhaust is also an option but with her slow / stun of her Equilibrium Strike, there's no point in it

For the phases of the game...
Beginning game is essentially what makes or breaks Irelia for the rest of the match. You do well there, you will carry into late game. Here's a little more in-depth for the entire game in a whole:
Beginning game is the hardest to get through. If you can get past that with a decent amount of farm, late game will be a breeze for you. Just be that initiator for your team and make sure to make use of your passive Ionian Fervor and soak up as much of the enemy's CC as possible and you are sure to win teamfights. Also, after you soak up all the enemy's damage, aim straight for the major damage source on the enemy team. Whether your team focuses the tanks or the damage dealers, you should always be on the hunt for the glass cannons in the back of the lineup. If you have to, pop Ghost. It's amazing for getting past the tanks and chasing down the fleeing squishies.
If you follow this method and do what your team needs you to do, winning teamfights and even the game will be very difficult to mess up.

Well, like I said earlier, this is only my first build / guide on MOBAfire so be patient with me until I get the hang of it and please comment and critique my guide as you see fit so I can improve for my future guides. Again, thanks to JhoiJhoi for making her epic beginner's guide (that can be found here), thanks to Minami for showing me to the above said guide and thanks for reading and hopefully I'll see you guys out on the Fields of Justice!