I'm just going to keep this guide simple. Like it or leave it, this is how I play Jayce and I have plenty of success with it. This build has allowed me to carry many poor teams and the worst case scenario is almost always losing with a half decent score. Jayce is my favorite champ so far as I never feel bored or powerless with him. Being able to switch between range and melee is both fun and effective.
Whilst Jayce certainly has the potential to be played straight damage I find he benefits best from being built tanky dps as it allows him to utilize both his melee and range forms extremely effectively. Jayce is versatile, fun and quite deadly. The amount of free damage he gets from his abilities is astounding and I've found that the longer he can stay in the fight the better. He won't deal half-@$$ dps like Dr. Mundo or amumu and his kit makes him extremely difficult to kite or avoid being last hit upon. In many ways, I consider Jayce the perfect champ when built this way.
Standard rune set up. Flat armor and magic resist give Jayce and every other champ for that matter significantly increased early game survivability. Flat armor is especially helpful when jungling.The reason I use a few magic per level and a few flat magic resist runes is incase I'm topping against an AP champ like Morde or Rumble and I want to increase my chances of getting first blood on them. Feel free to go all MR per lvl as it pays off later on. Whilst Jayce deals a fair bit of magic damage, I have no issue with the flat armor pen runes since the bulk of his damage is still physical. I'd imagine that hybrid runes would work well also. However, flat armor pen is particularly potent for his ranged q.
Shock blast when combined with the acceleration gate is one of the greatest harasses and damage dealing abilities in the game. It's range, speed and AOE effect makes it incredibly effective considering the amount of damage it deals. I think of it as a superior AD version of nid's spears. I level his w second because the AOE magic damage in melee form is beast as is his attack speed/damage buff whilst in ranged form. I max e last because it only enhances one damage ability which scales better into the game because it deals % of hp. I max his ultimate whenever I can because it increases such stats as tankiness, % armor pen and damage dealt.
Shock blast is great harass and great for last hitting. Always launch it through the acceleration gate as it's damage without it is fairly lack luster. Don't be afraid to use this ability point blank either. Unlike nid's spear, distance does not increase the damage dealt by this ability.
Hyper charge is a very nice damage dealer. Jayce's attack speed is maxed to 2.5 and deals more damage the more it's leveled. When building straight AD this is essentially Jayce's bread and butter as it deals massive burst damage especially when critical strikes are involved.
Acceleration Gate increases movement speed and increases shock blast's damage by 40%. The movement speed is nice for avoiding ganks and helping to initiate into melee engagements right after landing a shock blast.
Jayce's ultimate allows him to switch from ranged to melee form. When Jayce switches to melee form he gains armor and magic resist as well as dealing magic damage on his first strike. When Jayce switches to ranged form his first basic attack reduces the target's magic and armor resistance. All in all, good stuff.
In melee form, Jayce's q is To the Skies. This is simply a leap similar to Jax's that slows and deals attack damage. It's ratio isn't too bad, but not spectacular.
Lightening Field is potent enough that if you're not into shock blast harass then you feel free to max it first. It deals AOE magic damage per second for 4 seconds. It's quite a hefty damage dealer and clears minions well. It has a 1-1 ratio in case you want to build death fire, lich bane AP Jayce. I really want to see somebody do that on Fiora sometime...
Thundering Blow is a spectacular ability. Jayce swings his hammer and knocks back his opponent dealing magic damage based on % of hp. It also deals AD damage with a 1-1 ratio so it's a great ability on straight damage Jayce. Maxed out it deals 20% of a target's hp. Similar to such abilities as poppy's q and mundo's cleavers, this ability becomes a godlike damage dealer as it levels up. Last hitting with it almost becomes too easy. In conjunction with acceleration gate, this ability can make for a great escape tool as well save for that pesky olaf when he's ulting.
When in an engagement I generally initiate with a shock blast through the acceleration gate followed up by hyper charge. I then quickly switch to melee form and use To the Skies in conjunction with Lightening Field to close in on the target and deal out more damage. If last hitting with Thundering Blow is out of the question then wait until Jayce' ult is off cool down before using Thunder Blow and then quickly laying down an acceleration gate, launching a shock blast through it and chasing with hyper charge. With this tanky dps build the idea is to be switching between forms whenever possible in order to be constantly using abilities and dealing out loads of damage.
Flash and Ignite are my favorite summoner spells as Flash allows lots of utility whilst Ignite actually deals quite a bit of true damage and cuts health regeneration effects in half.
Ghost doesn't offer the same quick get aways and sudden initiates as flash does, but it does allow for consistent chase and when combined with Thundering Blow can make for a great get away spell.
Unless your concern is being kited, (as is often the case with Tryndamere), I consider Ignite to be better than Exhaust as far as dealing damage goes. However, Exhaust is a potent spell if damage is the least of your concerns.
Heal is just a bait spell. It's a decent heal and I've attained many kills with it, but it's usefulness is limited since it's healing effects are halved if your opponent lands ignite on you before you use it.
Smite is obviously a must in the jungle and the rest of the summoner spells are trash.
The items in this build are focused around gaining both survivability and damage with every item. I always build the frozen mallet first, but other than that the rest of the items can really be built in any order you feel suits the game you're in. If my main concern is AD, (and it often is), I build the Thornmail and if my main concern is AP then I build a Maw. Ideally I like to build a hex drinker first for the damage and survivability before building the Thornmail. The Wits End and Atma's are again both anti-AD and anti-AP items that also grant significant damage enhancers. I often find that the Maw is enough to appease any concerns I have for AP so there's a number of luxury items one can replace the Wits End with.
Why Thornmail over items such as Sunfire Cape and Randuins that will boost the damage gained from the Atmas?
The truth about the Atmas is that the bulk of the damage gained from it is your total amount of HP gained simply from leveling up which will be around 2300. Every 1000 hp after that will increase your damage by 15. I build the frozen mallet, (or warmogs), less because it synergizes with the atmas but more so because I want the survivability.
The sunfire cape will offer more hp, but significantly less survivability against attack damage champions because of your overall decreased effective hp. The extra 450 hp from the sunfire will grant an additional 7 AD from the atmas and the passive 30 magic damage per second. This can only be made effective against ranged AD when you can get to them.
I don't look at thornmail as a straight tank item but rather as a significant damage boosting item. On a 1000 critical strike the 30% returned damage will deal 300 magic damage per every attack ad champs make against you. (150 returned magic damage on 500 damage and 75 magic damage returned on a mere 250 attack damage). As you can see, the thornmail vastly out damages the sunfire cape/atmas combo. Granted, it only applies if they attack you. But if they're running away - good, they aren't attacking your team mates and if nobody wants to attack you because of the thornmail that's also good, because you're not a tank. Between all of Jayces abilities you have the damage to quickly kill any squishy champion without the need for an additional 7 AD and 30 magic damage per second. If you're yearning to deal AOE magic damage to the entire enemy team then I suggest playing champions like Mundo, Amumu and Karthus. But keep in mind that burst damage and 1000 crits win, not 150 magic damage per second.
As for the randuins it offers even less additional AD from the atmas and other than that is a straight tank item. Fun fact though is that because of the hp that comes along with it, it does grant more effective hp than a thornmail and it's passive attack speed killer makes it a potent anti-AD dps item.
And as a final argument in favor of the thornmail, it can be potentially effective even if you're not attacking the ad carry. Without at least 2 life steal items the carry will be killing themselves by attacking you and the 100 armor will allow you to eat the hits while you're destroying the tanky dps standing in your way.
Potent luxury items:
Warmogs - More HP, more sustain
Quicksilver Sash - Not the type of item I'd generally build on a tanky Jayce, but it's a nice and relatively cheap item all the same considering it's stats and active.
Guardian Angel - More armor, magic resist and two lives. A circumstantially useful item.
Infinity Edge - Because nothing amps up the damage on a tanky dps build like the best damaging item in the game.
Blood Thirster - Greater damage and sustain.
Last Whisper - For those teams that stack a **** ton of armor. In some games you may need to build this item sooner rather than later.
Black Cleaver - A nice overall damage boosting item. Depending on whether or not you're packing armor pen runes you're better off building a LW if the enemy has more than 105/130 armor
Spirit Visage - The ****... nobody even builds this item. It's so lack luster and garbage. Why doesn't this build into something better?
Starks Fervor - ... ... ...
Soul Shroud - Have you ever seen anybody, even one single person build this?
Leviathan - Trololololol
Jayce is a potent champ in the right hands. I'd be disappointed if he gets nerfed, but it wouldn't overly surprise me. Similar to Darius he can deal an incredible amount of damage without damage items, but even a little bit of damage goes a long way with him. If you want to see a squishy Jayce that wrecks **** just build an IE, BT and an Executioner's Calling. Good **** right there. In fact, try that on Wukong with a Brutalizer in the mix. It's insanity.