This guide is mostly based on the Ranged AD play style of Jayce because that's the style I enjoy most.
I will add a build for the alternate play style of Jayce once I've had some experience with it.
The build I use is pretty basic and is seen on most AD carries with slight variations but I do hope the guide helps.

• I chose Greater Quintessence of Attack Damage and Greater Mark of Attack Damage for Jayce because they are quite helpful early game to harass the other team and improve his overall Damage output.
• I also went with Greater Seal of Armor and Greater Glyph of Scaling Magic Resist to help with survivability, the Magic Resist saves quite a bit of gold endgame and leaves an item slot free, while the armor just makes Jayce that much harder to kill.
  Making it less likely for him to be killed early on.

Damage with a little Magic Resist and Armor.
It is the same idea as with my runes choice because to me it makes a lot of sense.

Feel free to edit them slightly, for example you could do the following;
Take 1 point out of Hardiness and put it into Durability
Or move a point from Alacrity into Demolitionist

Demolitionist is quite viable as a replacement Mastery because if you can combo nicely from both ranged and melee forms and like to take chunks out of turrets, Jayce is actually very good at it.

Now, the item build for Jayce is really flexible but Boots and 3x Health Potion can never really go wrong for the first time you leave the summoner platform.

The next part depends on how well you can harass the enemy team before you need to recall.
Of course though, don't get too greedy,
If the enemies you're laning against need to recall a few times, chances are they are picking up some items too.
So try to make sure you never have much more than 1000 gold at a time or you may fall behind.

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2x Doran's Blade is a nice first recall because the stats are just sexy for early game fights.

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On your second recall, you can either finish Berserker's Greaves or make Philosopher's Stone because boots aren't a big need when you can use Thundering Blow / Acceleration Gate

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For the third recall, you should have finished Berserker's Greaves and Philosopher's Stone plus spent the rest of your gold on starting Infinity Edge (Either buy B. F. Sword or Pickaxe)
If you have enough gold for a Vampiric Scepter pick one up too.

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Fourth recall now, the game should be close to the 25-30 minute mark, if it's not don't worry,
All games run differently.
This recall you should hope to finish Infinity Edge and be able to start Zeal
At this stage you need to think about what you buy though,
If you're being harassed a lot, build Bloodthirster now,
If the enemy team is building tanky, build Last Whisper instead
or if you feel you need to kill stuff faster, Phantom Dancer
You don't have to follow the guide at this part because games vary a lot and my recommendation could be useless.

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Now, this recall should be one of the last.
At this point you need to finish as many items as you can
Of course, keeping in mind what you need most.
And you can also decide what to do with Philosopher's Stone
You can either swap it into something with magic resist like Force of Nature
A lot of health like Warmog's Armor
Or extra attack speed and critical rating with a second Phantom Dancer

The skill sequence I go with is easy to remember.
You want to put 1 point in each skill early game, starting with Q, W and E.
Advance your To The Skies! / Shock Blast first,
Lightning Field / Hyper Charge second
And Thundering Blow / Acceleration Gate last.
While picking up a point in Mercury Cannon / Mercury Hammer whenever possible (6/11/16)

Now, This is where it gets tricky.
Hextech Capacitor Makes it so when you use Mercury Cannon / Mercury Hammer your first basic attack adds bonus damage.
So if you can combo this a few times in a fight it helps quite a bit.

You may not like this play style but this is how I initiate fights with Jayce
Start with Mercury Cannon / Mercury Hammer, make sure you are in Hammer form (Yellow)
Jump in with To The Skies! / Shock Blast
Hit Lightning Field / Hyper Charge and Thundering Blow / Acceleration Gate while en-route to the enemy to make them all go off at the same time,
to get in as much damage burst as possible.
All spells should now be on cooldown apart from your ultimate.

Once the player starts to retreat, hit Mercury Cannon / Mercury Hammer again so your spells are blue (ranged) version.
Make sure your first hit is on the champion for the extra damage
And follow with Lightning Field / Hyper Charge for the bonus attack speed.
With the next part, your opponent needs to be low, but if you can combo Thundering Blow / Acceleration Gate with To The Skies! / Shock Blast you get insane range and damage.
This combo is great for picking off long range kills, or harassing the enemy if they are turret hugging.

Also, Thundering Blow / Acceleration Gate can be used in team fights to either;
Speed your team up for a gank or to finish a kill
or to get away from a gank to put you in advantage.

Another way to cover some ground in the jungle, is to be in ranged form,
hit To The Skies! / Shock Blast aiming it over a wall into a group of nearby minions and reveal their position,
Quickly switching into hammer form with Mercury Cannon / Mercury Hammer and using To The Skies! / Shock Blast once again allowing you to jump at the minions.
This is great for jumping small walls to get to or from enemies or support allies in fights.

For summoner spells, I chose Flash and Ignite.
Flash is amazing because you can cover a decent amount of distance but the cooldown isn't too nice.
Ignite is great if you can get it on enemies before they die to get those risky kills you couldn't get normally.

I wouldn't suggest using any summoner spells apart from these but if you don't feel comfortable with them,
Feel free to choose something like Teleport, Ghost, Promote or even Heal and Clarity
It just depends what you feel more comfortable with.

Hey guys, this is my first guide for Mobafire so it may no be all that good but I thought I'd give it a shot.
Credits to Jhoijhoi for the guide I used to make this. Making a Guide
Thanks for reading my guide, feedback would be appreciated seeing as this is my first but may not be my last.

I hope this helped and I will do my best to improve it when I have time :)