The following advice is applicable for a short time until S3 starts:
Start Boots + 3 or Regen + Pot.
First back: Have boots + Philo stone.
Heart of Gold
Then in some order build:
Glacial Shroud (fix mana, get tankier, get CDR)
Aegis (much tankier and help team)
upgrade boots into either Merc Treads or Boots of Mobility.
Then in some order do these:
Upgrade Glacial Shroud to Frozen Heart.
Upgrade Philo into Shurelyas (you can do this earlier if you want, but you lose gp10).
Upgrade Sheen to Triforce.
Upgrade HoG into Randuins vs an AD heavy team, OR sell HoG and get a strong MR item if the enemies have substantial magic damage, or for a Guardian Angel vs a mixed team. (This one is last).
The entire time, buy a reasonable number of wards, and potentially buy oracles.
Boots of Mobility OR Merc Treads
Randuins OR Guardian Angel OR MRes item (Force of Nature normally, or Abyssal Scepter if no one on team built it and you have good magic damage dealers)
The build order varies based on the damage makeup of the enemy team, how early you expect teamfights to start, and whether you are ahead or behind.
If Ahead: Get sheen fast and increase jungle speed and gank power, aiding your snowball.
If Behind: Get tanky items first (Glacial/Aegis), so that you wont just die in a gank. You need this due to increased enemy damage. In a gank you no logner do much dmg, but you are a CC bot and hope your team can kill them. while you are tanky enough to live.
Against AD heavy team: Get the glacial shroud first (after gp10 items).
Against Magic heavy team: Push the aegis up the list/Merc treads up the list, and/or get an extra null magic mantle early that will alter build into those.
Also, your mid's desire or lack thereof for blue buff effects your build. If your mid needs blue ASAP (Anivia, Orianna, etc), then you need to fix your mana by rushing the glacial shroud first. But if your mid is not blue dependant (Katarina), then you should get the midgame blues and get aegis/sheen before glacial.
One final note: Top level players complete Shurelya's earlier than I do, while I milk the Gp10 longer and improve my damage and tankyness first. I would recommend this approach in non-high elo games, as it helps you be stronger later and carry your team more, and the teamfights tend to start later on the lower elo you go.
Wriggles is terrible on him. Hextech is poor. My build gets the game's best tanky/bruiser items like Frozen Heart, Aegis, and Triforce. The triforce alone gives you reasonable damage as your only damage item, while Aegis and Frozen Heart help your team SOOOOOOO much.
Ult when possible.
I put my first point in E at level 8 and then ignore it again until I have to rank it. Its bad and wastes mana early on. Pumping your shield more is better for sustain and damage.
Masteries: 0/21/9, with defense for minion dmg reduction, CDR, move speed, hp, etc. Utility for mana and mana regen and buff duration.
Summoner spells: Smite + Flash, always.