Jayce is made to wear down the opponent before he engages and is well equipped to do so. He can harass constantly with his Mercury Cannon in early laning phase without even spending mana, his E+Q combo in cannon mode does enough damage to make the opponent lose farm unwilling to get to close; while his Q+E in hammer mode slows the enemy, throws them to desire location, and even gives you bonus defensive stats so you take less damage then they do (It is key to swap to hammer mode when you're about to take a massive beating). My favorite combo is to always stay closer to the river (yes it's very risky so by wards and stay aware) and wait for your opponent to try to farm, pull up your speed gate (E in cannon) then shoot to where you know they will dodge towards (learn to predict movements every opponent is different) then run thru the gate, press E, and swap to the hammer (yes, it's clobbering time) proceed to use your Q as a gap closer, or save it for the opponents flash, either way use your W when you do it and run around him while he's slowed and use E to knock him back into your creeps. This burst is Jayce's only real source of damage (There is a reason there isn't an IE and a PD in a good build) that is why you have the tanky items to do it again and the item passives to make it even more killer.

The reason for the items chosen are to provide a good amount of damage after his massive burst attack and survivability (If the enemy is still alive to fight back). It may look like a weird build but it really works. Not only have I used it but my friends have used it as well and in each game they stomped they're lane (Top or bot (preferably top)).

Hope you enjoyed this guide and sorry I didn't do all the fancy stuff, I will try to in the future. Please don't leave any comments like "I would buy this rather than this" because every game is different and the ability to have a build planned out and alter it accordingly is part of what makes the good players good, no set builds only a brief plan to start with.