Simple Guide to an incredibly strong Sion build in the Bronze tier.

2 Variants, Full Tank and Off-Tank

Off-Tank is only recommended if you have been able to snowball early.
If you don't, Full Tank is better until you're comfortable with the champion.

I just use the cheap runes. Switching the Quintessences to %Health can give you additional health, but you sacrifice the ability to CS

Typical build will go along these lines.

Build order does not have to be exact. Build to counter your enemies, don't copy/paste a build path.

Full Tank
Doran's Ring > Spectre's Cowl > Sunfire Aegis > Spirit Visage > Frozen Mallet > Randuin's Omen > Titanic Hydra

Off-Tank
Doran's Ring > Tiamat > Ravenous Hydra > Spirit Visage > Sterak's Gage > Black Cleaver > Thornmail > Dead Man's Plate

Do note, that these are fairly generic, and are not secific to the enemy team comp. They are the usual build I will do, although there will always be variances to fulfill a specific need in different matchups.

Some Items to consider:
Warmog's Armor Black Cleaver Frozen Heart Rod of Ages Turbo Chemtank Frozen Mallet Randuin's Omen Banshee's Veil Titanic Hydra vs Ravenous Hydra and Doran's Shield vs Doran's Ring

Regarding the hydra twins, I enjoy Ravenous Hydra more, thanks to the extra Attack Damage it offers, as well as Lifesteal and Regen. However, the Titanic Hydra is far more effective for a full tank build, where it can benefit from your massive healthpool.

Regarding the doran's items, I suggest taking Doran's Ring over Doran's Shield because it allows you to poke the enemy with E Roar of the Slayer to proc their shields or just be a nuissance. I tend to poke every 3-4 minions, so 2x per wave. It keeps them on the lookout, and distracts them from CSing. (This operates under the assumption you will not miss CS, and will have Mana to burn. If you are not very good at CSing, I suggest you pracice that, but only poke once per wave)

If you are facing a heavy poke champ, like Aatrox or Ryze, a Doran's Shield is still a viable option until you are experienced with Sion. Doran's Ring is simply my preference since I play aggressive and like to punt minions around a lot.

Tips and Suggestions

Which Boots do you need? That depends entirely on your matchup. If the enemy team has too much CC, Mercury's Treads are essential. Vs High AD get Ninja Tabi
All else, get Boots of Swiftness for team fights, or Mobility Boots for roaming. Those two are not as useful as Mercury's Treads or Ninja Tabi, but still viable in certain playstyles.

Why so few attack damage items?
You're a tank.
In Bronze.
You don't need excessive damage.
Deal with it.

And considering it's Bronze, don't expect anyone else to know how to prioritize objectives or focus enemies. If they engage, move in with them. If they want to push a lane, help them. If they want Dragon or Baron, be there.

This shouldn't be difficult, all you need to do is protect them from as much damage as possible, without dying. Don't intentionally die to protect them, fall back when you get to 1/4 HP. Wait for your Regen to pick you up, or Back.

If you want to tower dive, type in chat that you are willing to tower dive. Tell them you'll signal when you're going in. If they don't follow up, and you're not super tanky yet, fall back and let them go. DO NOT CHASE if you have not caught them in 5 seconds, chances are good you never will, you'll just chase and leave your team wide open to the enemy. Stick to your teammates, let them chase if they want.

After winning a teamfight, focus on an objective. Prioritize the nearest Tower. Get Dragon, or Baron. Do SOMETHING to keep your lead, don't run back to lane to farm until you've accomplished something. (This is a pet peeve of mine. get a double kill? TAKE THE NEAREST TOWER. Don't back or wander to a different lane. Destroy an objective or help your team get an objective.)

Item Variation

If you have enough practice with Sion to use his E Roar of the Slayer effectively, (while CSing properly), Doran's Ring is my absolute favorite to start lane with. You can poke for the entirety of the laning phase, and still have mana left over for ganks. If you're bad at CSing, PRACTICE, and get Doran's shield instead.

Starting Doran's Ring, pick up E Roar of the Slayer first, and proceed the punt minion's into their face until they
A. Back
B. Die

If they dodge your puntacious minions with minimal effort, Max your Q Decimating Smash or W Soul Furnace first.
If you can land a lot of punts in a row, feel free to put a point or 2 into your E Roar of the Slayer before maxing your W Soul Furnace

Usually however, I will put a single point into E Roar of the Slayer first, and then proceed to max W Soul Furnace. I will only max Q Decimating Smash if I am doing very well, or I am building the Off-Tank build.

If your enemy laner or jungler are building armor pen. items, like Youmuu's Ghostblade or Maw of Malmortius, build an item with health first. This will help you in the short term, but you will still need some hefty armor items down the line. Frozen Mallet or Spirit Visage are my personal favorites until I can build a Frozen Heart or Randuin's Omen to properly minimize the effect late-game.

Health is your best friend. If you want to switch Frozen Heart for a Randuin's Omen or Dead Man's Plate, do it! It's entirely situational, but arguably your preference. I rarely get Frozen Heart because I value a gigantic healthpool more than an extra 30 armor. Frozen Heart's passive and CDR are the primary use for it, but that is if you are not able to sufficiently focus CC the enemy ADC to death.

Rod of Ages? Yes. If you are doing so well, it's laughably easy to kill your enemy laner with E Roar of the Slayer, RoA will make your day! It gives you Health (Wow!) Mana (So useful!) and more AP to punt harder (Inconceivable!). Granted, this is entirely a cheese* item, so build at your own discretion. If you do get it, you will need a Thornmail to compensate.

Banshee's Veil shouldn't strictly be on your list. You're the tank, you shouldn't be afraid of enemy abilities. If you absolutely, must have it, by all means. But Spirit Visage will give you more health, much needed CDR and better Regen. Leave the Veil to the ADC IMO.

Randuin's Omen vs Dead Man's Plate vs Sunfire Aegis
I like to rush Sunfire Aegis if I'm against an AD laner. It helps immensely with trades.
Dead Man's Plate can make your ultimate hit harder, as well as assist you in roaming. If you don't roam much, don't get it.
Randuin's Omen is the absolute best vs ADC crit late game. It also gives you some much needed peel. I strongly suggest getting this item around the mid-game, early game if the enemy team is AD heavy. Stack with Thornmail in such circumstances.

A well timed E Roar of the Slayer > Q Decimating Smash > W Soul Furnace can easily chunk the enemy tank, or outright kill a squishy. Prioritize the enemy ADC or Assassin, whichever is closer. If you are unable to reach them, fight the front line and protect your team from skillshots and as many abilities as possible. Dish out some Punts into their backline while you're at it.

Black Cleaver is a situational item on Sion. If you need team Armor shred and CDR, it's useful, but it's generally outclassed by Frozen Mallet and the better tank stats it provides.

Warmog's Armor is a great choice as a last/second-last item, it'll keep you in lane forever, and you'll never need to back if you don't die. This stacks nicely with Titanic Hydra and Frozen Heart.

Grab Blue Buff if you need mana at Late-game, but you should save your abilities for engaging, not wave clear (with exceptions. Use judicion)

And of upmost importance, YOU CAN'T HIDE BEHIND LACKEY'S