Your Win Condition
Your goal is to conserve health early on, let him push, and then look for a level two all-in with Q and W when the wave settles. If he has Phase Rush, the win condition shifts to successfully executing an all-in when his Phase Rush is on cooldown. You should try to trade your Ghost for his Flash in the early all-in.
General Strategy
You should run Doran's Blade with Ghost and Flash. Conserve HP early game by letting him push you in. The strategy is often described as 'fishing': if you hit the axe, pop Ghost and commit; if you miss, wait for the next opportunity. If he utilizes Phase Rush, play around that cooldown.
Trading Patterns
Use cheeky auto attacks onto the wave and Q the minions to damage him simultaneously. If he has Phase Rush, you must use a two-trade rotation: Q and run at him (to proc PR), run away instantly (even if you leave your axe behind), and then all-in him on the next Q when Phase Rush is down. If he doesn't have Phase Rush, it's all about hitting the axe, popping Ghost, and committing.
Wave Management
You must let Jayce push you in early game. Avoid trying to get priority, as this will lead to you taking too much poke damage. When the wave is near your tower and you hit level two (QW), look for the all-in.
Their Win Condition
Jayce wins by poking you down heavily before you can force an extended trade. If he takes Phase Rush, he wins by kiting you effectively and preventing you from getting onto him.
