Jhin is a low mobility, high skill cap champion that offer large burst damage and support but lacks consistent dps pressure. He excels with long range damage and setting up plays for his team. His unique passive allows for a large variance in builds as well as starting skill order.

Dancing Grenade - Level 1 lane presence (recommended)
Deadly Flourish - Jungle Invade
Captive Audience - Additional Jungle Leash with passive level 1

Levels 1 -> 3
Q > W > E - Standard start
W > Q/E > E/Q - Depending on lane. Take Q for aggressive E for passive
E > W > Q - Passive Lane may draw early gank. Take Snare 2nd to be safe

Skill Max Order
Curtain Call - R - Ultimate
Dancing Grenade - Q - Good for farming during reload
Captive Audience - E - Extra magic damage scaling of AD
Deadly Flourish - W - No real benefit in maxing

Starting Items
Doran's Blade/ Cull

First Back
Serrated Dirk
Boots

Core Build
Duskblade of Draktharr -- Gives more burst damage and assassination ability. 10 Armor Pen
Berserker's Greaves - Furor/ Boots of Swiftness - Furor]]
Youmuu's Ghostblade -- Great active. 20 Armor Pen
Lord Dominik's Regards/ Mortal Reminder -- Pick one vs either armor (Malphite) or healing (Mundo)
Runaan's Hurricane -- Limited amout of shots. Great for spreading damage in a team fight.
Infinity Edge -- Decent all around item. Adds to passive damage and gives additional crit damage.
Farsight Alteration -- Great item for ADC. Can be used during Ultimate

Situational Items
Sterak's Gage -- Good Vs Assassins
Death's Dance -- Better for lifesteal than Bloodthirster
Mercurial Scimitar -- Good for CC
Rapid Firecannon -- Decent item but no added benefit that a core item does not give

Item's not to get
Essence Reaver -- Jhin does not need CDR late game
Bloodthirster -- Death's Dance is better used for Jhin's kit.

Try to CS using only Auto Attacks.

While reloading, kite away from enemies.

Use Dancing Grenade to last hit when reloading.

Dancing Grenade does more damage after it kills a unit. Set up the minion wave to kill one or more minion to increase efficiency.

Dancing Grenade can do decent damage to enemy champions. Kill all melee and cannon minions then bounce Dancing Grenade of the casters to harass.

Use Dancing Grenade in a duel before you fire your 4th shot. This will increase the passive damage on the 4th shot.

Deadly Flourish and Captive Audience can be cast while reloading to maintain DPS.

Deadly Flourish can be used to last hit minions while walking back to lane.

Captive Audience puts a marker on enemies when then enter the circle of influence. Time this with Deadly Flourish to snare enemies in the AOE damage.

Curtain Call slows enemies. You can assist your team in chasing by landing even a single shot.

Farsight Alteration can be used during Curtain Call to help spot enemies in Fog of War

Jhin is highly flexible in build path. Consider the enemy team when going down a build path.