Pros don't want to die. You don't want to die, but you will die. Fortunately for you, Sion synergizes with dying, and this build capitalizes on that highly probable outcome. Take smite for the Tenacity Jungle Item. It gives you Cooldown Reduction, which isn't in Dota (OP), HP (synergizing with your infinitely scaling HP and %HP Seals), TENACITY (which you need in conjunction with Boots of Swiftness, for your Glory in Death "zombie form"), and eventually, champ smite.

Take Ignite, because you will die, and when you do, you want to send a message. The message could be: "Whenever your jungler tries to gank me, I get a double kill." That's a good message to send.

Starting Items

Start with Crystalline Flask, an HP potion, and two mana potions. This allows you to stay in lane for a long time, stacking that infinitely scaling HP, and harassing your opponent with your E constantly with those Hybrid/Magic Penetration runes.

Early Game

Stalker's Blade-Juggernaut: The reason for taking Smite as a summoner spell. Gives you HP, CDR and, most importantly, Tenacity. HP works with %HP runes, CDR works towards the 40% cap, and Tenacity allows you to maximize damage output during Glory in Death "zombie form". Champ smite is just icing on the cake, and is basically a second ignite. If you're going to die without defensive summoner spells, might as well get a double kill.

Boots of Swiftness-Alacrity: Simple. Extremely fast IN combat + slow resistance = optimal Glory in Death "zombie form". Works with Tenacity incredibly well by reducing the intensity AND the duration of slows.

Frozen Mallet: The one "must build" item on Sion, since his autoattacks in "zombie form" will slow your target, keeping you healthy and them unhealthy.

Core Items
Black Cleaver: Works towards the CDR cap (more slows/ults), offers flat and % armor pen (Glory in Death %HP physical damage), gives HP (%HP runes), and gives AD.

Zeke's Herald: An unpopular item. Maxes your CDR (more slows/ults), gives HP (%HP runes), AD, and lifesteal (prolongs passive). The fact that the aura benefits nearby teammates is icing on the cake.

Infinity Edge: The only optional item in this build (see recommended alternatives). I prefer it because it offers the most damage output and works very well in "zombie mode" (a 250% crit with 100% or more lifesteal keeps you alive much longer). Plus its always fun to see Sion finish someone with a this is Sparta dropkick.

Start with Soul Furnace to begin stacking HP right away. Begin maxing Roar of the Slayer to harass your opponent to no end. Less experienced players will see that you have no AP, and are building AD. Despite getting poked for tons of damage, they will build armor. Soul Furnace scales incredibly well into late game (thanks to Magic Penetration), because it deals %HP magic damage.

With 3 ranks in your ultimate and 40% CDR, Unstoppable Onslaught will be on a 36 second cooldown! Exploit that for lane pushing, ganking and objectives.

Mostly offensive, with just enough defensive to get the %HP mastery (infinite scaling HP). Sion already scales infinitely in defense, so maximize your offense and exploit his ridiculous poke/gank/passive potential.

All of Sion's abilities proc the Blade Weaving mastery, and conversely, every ability benefits from the Spell Weaving mastery. Exploit that! Auto-attack your enemies before popping your shield to magnify your %HP damage! Do some more auto-attacking after using with your abilities to magnify your attack damage!

Hybrid Pen quints/reds, because he deals a lot of physical damage (not to mention %HP physical damage during Glory in Death), and because of his shout-poke magic damage, and because his shield deals %HP magic damage that scales with the ability level.

Magic Pen blues, because of the afore-mentioned shout-poke magic damage and %HP magic damage from his shield.

%HP yellows, because his HP scales infinitely. It's a no-brainer.

Warmonger Sion, because it is the most try-hard skin attributed to Sion.

Omg ban Vayne. There are plenty of champions who deal %HP damage... but %HP TRUE damage? Omg op ban Vayne immediately gg.

Try it before you criticize it. Poking in lane by launching minions takes some practice, but landing the hits is incredibly rewarding. Look at the damage graphs post-game. I consistently get the most in "damage to champs" and "damage taken" (which can actually be a very good thing to have, considering infinitely scaling HP + %HP runes).

Goodluck and happy carrying.