Hey ya'll. This is my first ever guide and I thought, lets begin with Jayce.
Jayce is a really awesome champion imo. I directly spent my ep on him and none of it is wasted! You can play as everything with him, so as Top Lane, Bot Lane, Mid Lane and Jungler.
The way I play him is mostly in his Mercury Cannon, especially in early game to farm a lot and harass the opponent and yeah, as soon as the other champion has not much left, they get to know then his ultimate Mercury Hammer. Where I prefer to play him is as solo top, since you can annoy your opponent competely with your Mercury Cannon style, especially with the combination of Acceleration Gate and Shock Blast and as soon as they don't have too much hp, switch to Mercury Hammer, jump to them with To The Skies!, and just give them the rest with Thundering Blow in combination with Lightning Field.
So as you can read, it's pretty easy to rock with him, as soon as you know how to play him. But yeah, I hope this build speaks for itself if you try it and make you like to play Jayce even more :-)

Well, the Items, why did I choose these items. I can tell you why.

• The first items I buy are Boots and 3x Health Potion. The reason why I rarely ever begin with Doran's Blade is because I trust my runes. I am pretty sure of them and I can rely on them perfectly and Jayce's skills are strong enough too. So Doran's Blade is just a waste of money at this point imo. So, after you bought your items, go to your lane and farm around. Get your money and level. As soon as you got your money, buy Mercury's Treads. Why these shoes? Well, you will use ur Hammer later on too. And ofc. the others will run away from you because, admit it, you will be damn awesome. So to go after them better, you buy these shoes because screw their slow's and such. As you can see, it's more for the tactical use.
• After you got ur shoes, make them fear you. You do that slowly by getting your Trinity Force. Why I chose to get this item is because, it's the perfect alrounder Item and fits to Jayce really well. It gives him all he needs, HP, damage, attack speed and even a lil bit AP for your Lightning Field. And also you have a 35% chance to slow the others, which is only in your advantage. But which items will you buy first before you can finally upgrade them all to it? Well, I do it like this:
  1. Phage because you will need to increase your damage and your HP, so you can survive better and make them start to fear you.
  2. Zeal because you can farm faster and better like that.
  3. Sheen because it's the last item needed for Trinity Force, duh.
  And voilá, there you go.
• The next item you need to buy is Warmog's Amor. Why I chose this item is because, at late game, you will go for your Mercury Hammer really often, to kill the others fast and with style. But without HP, you will only be able to do like 1 - 2 kills. After you got ur enemy learn to fear you, they will most likely end up focusing on you, which will make you end up as a joke later on instead of the boss you are supposed to be. So, HP is totally needed. You may ask, why not Frozen Mallet. Well because, your Trinity Force already slows them and Warmog's Amor gives you more HP and even more through its passive. So it is not needed. And thanks to the lil side effect of Warmog's Amor, you will receive more and more HP and HP regeneration. The way I buy the needed items is buying Giant's Belt first, then Ruby Crystal and then directly Warmog's Amor. So now, we got the surviving strategy done. Lets go for the damage part now!
• Bloodthirster is a must have for every AD Champion. Nuff said. Damage and life steal. No more words needed about that! The way you buy it is up to you. I prefer to get Vampiric Scepter first because, you need life steal. And Jayce's skills already deal enough damage, so that sword can wait. But yeah, up to you.
• Maw of Malmortius because it can give you lots of extra damage and protects you. Some maths right here. Lets take the max. HP you see at my Guide, 3210 HP at level 18 (but it will be way more if you play him right thanks to Warmog's Amor). You get +1 on damage for every 2,5% health missing. So, without making it complicated, lets put it like this: 3209 * 2,5% = 80,225, means you can get till like 80 extra damage if you survive and kick butts with 1 HP. Unlikely to happen the 1 hp case, but it's just theoretically. And because you will have more and more HP thanks to Warmog's Amor, it will also mean, the extra damage you can get will also increase more and more! Gotta love logic and maths. So yeah, now you know why this item.
• The last item. Well, you can choose which item you want to use as last item. The last item can be totally flexible with Jayce. That's what makes Jayce even more awesome. Depend the last item on the other champions. As you can see, I showed you above to buy Black Cleaver. You can buy it ofc. if you want to go for damage and the other team is no real threat or doesn't have many damage dealers. So you can't be wrong with this item, since it gives you damage, increases your attack speed and even lowers the other's amor. But if the other team is i.e. (nearly) only AD based, it is better to buy Thornmail instead of Black Cleaver so they deal damage on themselves if they focus on you, which also means you can kill them easier too. If you want to be increase your amor and magic resist and be even more tanky, you can also go for Guardian Angel and even get revived, which is also not bad. If you rather want cooldown reduction, go for Randuin's Omen instead and receive even amor. So yeah, the last item is depended on the situation late game. There you can be creative ;-)

Mercury Cannon As you can see there, if you want to use your cannon at first, I focus first onShock Blast to make them fear it, even more when it's used in combination with Acceleration Gate. Then you focus on Acceleration Gate because you also need to consider your Mercury Hammer, which you will have to use ofc. too. And fact is, that the e-skill on your hammer, so Thundering Blow, is the strongest skill you have there. That's why you will have to skill Acceleration Gate before you finally skill Hyper Charge, which will deal really good damage after you skilled it fully. That's the skill sequence guide if you use your cannon first.

Mercury Hammer As you can see there, if you want to use your hammer at first. You begin withTo The Skies! to screw the distance between you and the opponent and then I focus first on Thundering Blow to make them fear it and make tanky champs fear you even more! Then you focus on To The Skies! because you also need to consider your Mercury Cannon, which you will have to use ofc. too. And fact is, that the q-skill on your cannon, so Shock Blast, is the strongest skill you have there. That's why you will have to skill To The Skies! before you finally skill Lightning Field. That's the skill sequence guide if you use your hammer first.

Well, these runes and masteries speak rather much for themselves. The classical AD runes and masteries. Always fitting, alwaays helping you to pwn. So, nothing special to say about it.

Jayce is perfect for team work. While using Mercury Cannon you can harass every opponent while you all wait to strike and then, after the others lost enough damage thanks to your cannon, you can switch to your Mercury Hammer, tank them unexpected thanks to To The Skies!, because you will have lots of HP, you won't have much to fear at tanking, and kill them all with your team. Every team will be happy to have you then!

Well, all in all, Jayce is a damn good champion, who can counter many champions on solo top i.e. He is the perfect allrounder and I hope with this build, he is it even more! Now that you know, how I play him and such, and learning how to play strategic with him, I believe you will also rock the game, like I do mostly with him. Here a proof of my last games with him:
Well, since I am German and way too lazy to find out how to change language, you gotta live with this picture :-P But I think, it speaks pretty much for itself :-) You can't do much wrong with that build, at least I didn't have many problems.
I will ofc. update this build as much as possible and yeah, for now, have fun with this Jayce!