Sion has the obvious tendency to become a tank because of his W passive and his CC abilities. The standard Sion philosophy is 'he gets beefy, so make him a tank'. This works as a toplaner, and can be a strong way of building Sion. This is not the philosophy of my build.
My philosophy is, 'if you get health for free why pay for it'. Sion gets lots of health naturally from his W passive, so it doesn't make sense to buy more. Instead, buying damage and juggernaut items turns Sion into a damage dealing powerhouse. At full build you will likely have 7k or more health, and you are dealing huge amounts of damage on your R, Q, and basic attacks. So don't buy that Randuin's Omen, buy Trinity Force and kill them.
I hope you enjoy my guide.

Why no boots? Because boots are expensive and Sion doesn't need them. For roaming and clear speed Sion has Youmuu's Ghostblade, Dead Man's Plate, and Trinity Force as items, and takes Relentless Hunter in the domination tree.
Not buying boots speeds up Sion's item powerspikes by 1100 Gold.
That being said, if you need Ninja Tabi or Mercury's Treads to counter the enemy team then go ahead.

When pathing your goal is to hit Birds and Krugs as many times as you possibly can. The ideal path (red side) is Blue (with leash) - Wolves - Birds - Red - Krugs. Blue side Red (with leash) - Krugs - Birds - Wolves - Blue works OK. You can gank mid after birds if your laner is pushed in.
Never bother with Gromp. He only gives 15 extra life and is harder to kill. Wolves give 23 life. Birds give 35 life. Krugs give 51 life.

While it may look like the items are weird, they are very thought out. Every item at each point in the game either plays to Sion's strengths, removes his weaknesses, or both.

Sion has several strengths as a jungler. He has strong early damage, and a healthy early clear. He also has several weaknesses. He has low MS, which slows his clear, and finds it hard to gank pre lvl 6.

Start by building Skirmisher's Sabre. You need the tooth and nail passive for clearing, and getting red smite is a dueling powerspike. However DO NOT upgrade it to Enchantment: Cinderhulk. Why? Because in the early game Sion has low health and high damage. The passive from Cinderhulk is wasted until Sion's W passive has racked up some extra health.

Your first full item is Youmuu's Ghostblade. Why build Ghostblade on a tank? Because Sion isn't a tank, he's a bruiser. And in the early game he does a lot of damage. So Ghostblade doubles down on his early damage, and also fixes his low MS and lack of roaming. The passive 40 out of combat MS goes a long way speeding up Sion's clear. The active can be useful ganking, escaping, and making the zombie more sticky.

At 1.5k gold after Ghostblade the enemy team are getting their items and you start to feel like a glass cannon. Upgrading to Enchantment: Cinderhulk fixes that, and makes your clear truly effortless.

Next start building Trinity Force. Sion needs stats, and Trinity Force has that in spades. It gives more MS, more damage, 20% CDR, more attack speed, and makes the zombie sticky. This makes it a huge powerspike for Sion. But doesn't it make you a glass cannon again? No, because your W passive has been busy racking up health from Krugs. After finishing Trinity Force you should be around 3k HP. With almost no resistances you aren't a tank, but 3k health is still a lot to go through and you are punching back with a force. You are a super strong bruiser, and if you die in a teamfight the zombie still does hefty damage.

The next two items can be flexed, depending on if teamfights have started or not. Sterak's Gage is my go to item after Trinity Force because the extra health means a huge amount in a teamfight. It also does a good bit of damage, and is a super solid item. But if you aren't teamfighting yet then Dead Man's Plate should be built next. It gives extra MS and some much needed armor.

As mentioned above, Dead Man's Plate should be built next. With it you have 464 out of combat MS (no Relentless Hunter stacks), and the armor combined with your 4k+ health means that you are truly a tank. You can take a full MF ult with ease, and you have great roaming power.

The last item to be built is Titanic Hydra. It is obviously a great item on Sion, so why wait so long? Because it is never really needed. As a last item it is the icing on top the the cake, turning Sion into a juggernaut capable of decimating an enemy team with 7k+ health to boot. Most junglers who buy Titanic do a Tiamat rush to clear faster, which Sion doesn't need. Thus Titanic Hydra only gets built at the end of the game.

Ganking is a hugely different animal before and after lvl 6.
Before level 6, to gank you rely on hitting your E on a pushing enemy laner. If you hit E you should be able to land Q or burn a flash. If you land Q they probably die, and if they burn flash you are happy anyway. But if you miss E or the enemy is under tower there isn't much you can do.
Pre level 6 the best thing you can do is farm Krugs and counter gank. While ganking is hard, counter ganking is easy as long as you are near the lane. You will likely get a kill off of a counter gank because the enemy team will chase your laner into your E Q combo. Ignite and Smite as necessary, and you have yourself a kill.

After level 6 ganking becomes a lot easier. If the enemy laners are pushing, just ult up the lane and kill them. This is especially strong bot lane, because at best you hit both the ADC and support and if they split up their ADC is an easy kill.
Try not to miss your ult tho, or you will look like a total idiot.

As Sion taxing is totally fine. You get more health when you kill the minions. Push the lane and get some Turret Plating gold. However, if your krugs or birds are up, leave that lane and go take your camp.
As Sion you shouldn't KS. If the enemy is going to die just E them to prevent them from escaping and let your laner take the kill. But on a successful gank don't be shy about taking the kill. Its okay if your laner gets it, but you need gold to finish your items.