First of all this is a remake to my previous Sion build with more in-depth detail and alterations based on feedback and additional research.
Think of this as a guide for the item build instead of a build for the Champion (im fairly new to Sion but i do have a exceptional talent at finding item builds that work very well).
The mobafire cheat sheet is wrong and needs to be fixed.
The final item line up should read Phantom Dancer > Phantom Dancer > Warmog's Armor >
Infinity Edge > Atma's Impaler > Frozen Mallet. Reffer to the Items Chapter.

This build is cheaper and the items are much more interchangeable than the original guide (mobafire.com/league-of-legends/build/the-6k-hp-crit-killer-175171).

Sion has a passive on his E ( Enrage) that gives you permanent hp per minion/champion/monster kill, depending on the ability level. This guide utilizes Sion's E to net him 6k hp with a bit of effort, once the build is finished and you have obtained a Warmog's Armor and a Frozen Mallet.

The runes are mostly for crit damage and a little bit of crit chance if you decide to jungle instead of lane.

I preffer crit damage runes because i believe you can do more damage to squishies and off tank champions than you could with armor pen. It's popular to take armor pen instead of crit damage runes in order to give you a better start in the match while laning or jungling but since i never even buy boots i find Sion gets much less hits in on the enemy champion so early game dominance is much harder to achieve without specific lane partners. In my opinion crit damage stacks better in late game rather than armor pen in early game.

Despite my protests against armor pen it's still a viable option to consider if you think it will be more difficult with your lane partner or if you decide to gank earlier than normal while jungling.

Crit chance is not entirely necessary but i find it gives me a better chance to jungle without taking Cloth Armor. A little bit of armor pen or attack speed in it's place may also be a good choice depending on your style of play.

Masteries dont matter too much as long as you try to prioritize crit damage and hp.

The skills i have chose are mainly for a jungle Sion (because getting kills early on helps better with overall hp) but i suggest taking and maxing Enrage asap for laning while getting Cryptic Gaze at level 4 instead of Death's Caress at level 4, also take Death's Caress at level 2.

That Ultimate, Cannibalism is deadly and a lifesaver if used at the right time. If anything this skill somewhat makes Sion with this build into a support champ but without Cannibalism he doesn't do anything to support and can be poor at ganking if you aren't a pro at ganking (not going to add "how to gank" since i haven't much experience at ganking).

Exhaust and Ghost. I take these two spells even when jungling because Sion isn't an incredible ganker.

I favor Ghost most because Sion needs to run fast or slow the target on hit in order attack a running champion (without boots that's harder than it seems in the beginning) with his melee attacks. Exhaust doesn't help quite enough with this because it only lasts a few seconds where as Ghost lasts 10 seconds and allows you to get many more hits in.

When in lane Sion can escape fairly easily without using these spells, assuming he doesn't over extend but when the enemy over extends he pretty much needs to use them both to get a kill (even if you choose to get boots).

I would only suggest Flash as a substitute because of it's many uses but only instead of Exhaust. The ability to jump over walls, get to the other side of a turret, leap over a crowd of minions or just to catch up to that elusive champ and stun them can be exactly what you are looking for.

For jungling you may not need Smite but it greatly accelerates the process and allows you to take the dragon down at level 6. I take Smite instead of Exhaust but it limits your ganking potential considerably, however.

The items i get for Sion aren't completely the best way to go but i find work very well in synergy with his abilities and in the long run cheaper for having not bought boots. Also to note is that the two Tiamat can be excluded if you haven't amassed enough gold before team fights start, which can even greatly change the order in which to buy each item. In this section I'll explain the reasons for each item and the order in which i buy them.

Brawler's Gloves - I take Brawler's Gloves at the start when laning with any Carry champion as a partner (ranged carry preffered, although i have found dps off-tanks like Garen work best with Sion). The 8% crit chance may not be much but it can change the course of early game battles in your favor easily because of Sion's Enrage ability. When jungling i take this along with 2 Health Potion.

Dagger/ Zeal - Next you want to work your way up to a Zeal so if you happen to get harassed a bit too much while in lane you may be forced to go back to base and heal, may as well buy Dagger while you are back at base if you can't afford Zeal right away. I rarely ever buy Dagger alone and usually go straight for Zeal as soon as i can. Zeal is important, it gives you additional move speed, attack speed and crit chance, i usually get it as soon as i can afford it. When jungling i go back to the spawning pool as soon as i can afford Zeal as well.

Zeal - get a second Zeal as soon as possible (starting with Brawler's Gloves if you happen to be at the spawning pool while being able to afford one). After the second Zeal you will be moving at a speed equal to having Boots but attacking faster and getting crits at a decent rate. When junlging i go back to buy the second Zeal before i start ganking.

Cloak of Agility - I usually have to go back to the spawning pool when i can afford this so i do so and gain the 18% crit chance it offers which makes you significantly more dangerous.

Phantom Dancer - Finally finished one, now you are running decently fast (about the same speed as the common level 2 boot, ie. Mercury's Treads, Ninja Tabi, Berserker's Greaves). Your attack speed exceeds 1.0 and your crits happen often enough to 1v1 if you run into to anyone unexpected.

Cloak of Agility/ Phantom Dancer - Just buy Phantom Dancer if you can afford it, no need to buy
Cloak of Agility unless your already at the spawning pool. After the purchase of a second
Phantom Dancer i am able to run at 416 and attack at 1.3 - 1.6 (depending on champion level) and crit at a 60% chance. When jungling this makes you a lethal ganker as well as a quick jungler though it's almost time to stop jungling at this point if you haven't been ganking much and haven't gained gold quickly enough.

Tiamat x2 (Optional) - Assuming team fights haven't started yet i decide some quick farming is just what i need to help push towers and slaughter creeps as quickly as possible to help my passive hp gain from
Enrage and gain a significant ad for my crits. Start with Pickaxe because it costs half as much as
Tiamat but will offer you some valuable ad, i only take a Pickaxe if i can't afford Tiamat right away which often happens for me. Remember to get 2 Tiamat if you bother to get them at all and sell them both at the same time to get 2900 gold for one of your later items. I take these while jungling as well if it's still time appropriate.

Warmog's Armor - Probably your best item for surviving team fights, the sooner you can afford it the better though if you need an extra boost of damage in team fights get your Infinity Edge before
Warmog's Armor.

Infinity Edge - Damage, crit chance, crit damage and roughly 3800 Gold. Infinity Edge is a must for this build and your last core item in the build (Core items: Phantom Dancer x2, Warmog's Armor,
Infinity Edge).

Atma's Impaler - As soon as I buy Infinity Edge i immediately sell the 2 Tiamat and buy
Atma's Impaler unless my team is having problems catching enemies in which i save up 400 gold then sell the 2 Tiamat to buy Frozen Mallet. I have 5k hp at this point (4k if you didn't buy the 2 Tiamat) which gives me 100 ad from Atma's Impaler. You will also note that your crit chance is 100%.

Frozen Mallet - Last item, this helps you get the Ace from every team fight which makes for an easier win. If you happen to run into someone in the jungle they wont be able to escape.

In this section i will explain some items that should helps you in certain situations and which item to remove from the build.

The core build should stay the same which means you have 2 interchangeable items which are
Atma's Impaler and Frozen Mallet.

Thornmail - If the enemy team is winning and they are heavy on AD i suggest take Thornmail instead of Atma's Impaler. The reason for choosing Atma's Impaler instead of Frozen Mallet is to ensure that the hits you take from your opponents deal as much damage as it can back to them. The Lifesteal you gain from your ultimate will help you survive while dealing massive damage back to your attackers, it's quite entertaining to watch your enemy confused to how they lost.

Guardian Angel and The BloodThirster - If the enemy team is winning and they are heavy on AP I subtitute Atma's Impaler for Guardian Angel and Frozen Mallet for Bloodthirster. The reason for Guardian Angel is to take burst damage and survive then activating your ultimate to fill up your health bar and kill them back. I take Bloodthirster to gain an extra 100 ad and 25% more lifesteal so i don't go down as easily before Guardian Angel takes effect as well as possibly taking an enemy down with me before rising again.

Bloodthirster and Phantom Dancer - When your team has good CC you wont need any so you probably shouldn't bother with Frozen Mallet. Instead take a Bloodthirster though you have less hp the 25% lifesteal should compensate nicely. Since you have less hp you may as well get a third
Phantom Dancer instead of your Atma's Impaler. More attack speed, more move speed, while still hitting with 100% crit chance but now you can catch any runner when you use Ghost and you can stun them to help your teammates catch up, you can also Exhaust if you really need to.

To Start (this portion will only cover the first 6 levels and Dragon) i Take Ghostwalk and Smite. Take Brawler's Gloves and 2 health pots. Take Death's Caress at levels 1 and 4. Take Enrage at levels 2,3 and 5. Take Cannibalism at level 6. Take Cryptic Gaze at level 7 (this ability hardly helps jungling at all but is nice for ganks).

I start with wolves (use smite on the brown wolf and death's caress only once per encounter), wraiths then Golems (smite the large Golem) then loop around to wolves and repeat a second time. Try to use your potions when you fall below 300 hp. Afterward you will be able to afford Zeal, go buy it and up to 5 hp pots or as many as you can afford then take down the Ancient Golem (use Smite) for Blue buff (since blue buff has high mana regen you can use Death's Caress during the fight as much as you need). Now kill the wolves and don't forget to abuse Death's Caress. Kill the Wraiths. Now it's time to use Smite on the Elder Lizard for the red buff. After you can afford another Brawler's Gloves, buy it then you can go gank effectivly or you can continue jungling. If you chose to jungle you need to go for the enemies blue buff most likely, so take it then head back to your jungle. Kill your golems, wraiths and Wolves without using smite. Now go into the enemy junlge again and take their red buff. By now you should be level 6 and can afford a second zeal, go grab it then fight the dragon alone (cause you don't need no help).

With Leash. Get the same set up as before except start with the blue golem.

Try to make sure you are not soloing as Sion, he does poorly with this build at the start (for surviving) if he doesn't have a good lane partner. I suggest Sion should lane with your ranged Carry or an off tank with good CC (Garen works well for me). The skill sequence also changes.
Engrage at levels 1.3.5,7,8. Death's Caress at levels 4,9,10,12,13. Cryptic Gaze at levels 2,14,15,17,18. Cannibalism at levels 6,11,16.

If you are losing in your lane you should omit the tiamats entirely. Hug the tower. Once you get Cannibalism and two Phantom Dancers you should be able to dominate your lane easily if your enemies were previously cocky. Stay alive, don't let them kill you and they won't be able to get fed.

Pros
+ Strong and fast with an ultimate that grants complete lifesteal.
+ core build works well in any situation.
+ Great item synergies.
+ Can 1v2 and win.
+ no boots but still just as fast.

Cons
- Prone to burst damage.
- Often highest priority target.
- Expensive alternative to boots.
- poor ganker.
- poor CC.