I've been trying Shen lately. People seem to suggest either Sunfire Cape or AP like Rylais. Needless to say, I'm confused.

Someone help me with item build, and maybe come up with a bit strategy as well.

Boots for the situation, which ends up to be either ninja tabi or mercurys.
Aegis.
Randuin's omen.
Banshee's veil just a negatron cloak, or a force of nature versus a caster team. Get anti caster items first if the really have a lot of magic damage.
Something like sunfire, or thornmail versus physical.
Finish with guardian angel.

That's a pretty quick and rough Shen build.

It really depends on the enemy team set-up and their builds.

First ask yourself what boots you need: Ninja Tabi or Mercury Treads. Don't be afraid to switch boots later on if you realize you made a mistake here.

From here on, your build should depend on the primary source of damage from the enemy team.

Mainly physical damage: Randuin's Omen, Sunfire Cape, Thornmail, Guardian Angel (Don't forget to use Randuin's Active Ability; it's a nice one!)
Mainly magic damage: Banshee's Veil, Force of Nature, Guardian Angel
If they have mixed damage, just take some from both.
You could also put an Aegis of the Legion in somewhere, but that item is preferred on a different character.
You are also expected to buy an Oracle if the enemy team has a stealth character.

You can't really tell a tank what to build; it's all situational. Banshee's Veil is a solid choice against almost any team composition. Check which enemy has most kills (Both human and minion kills) to decide whether you should focus M.Resist or Armor.
I wouldn't recommend any AP, AD, or similar stats: Go full tank.

Note on Guardian Angel: It's not supposed to be an 'Oh, I died! Luckily I have a Guardian Angel'-item. You die on purpose, let the enemy waste all their skills on you while the rest of your team picks them off, and you happily survive because of your GA.

Assuming a balanced enemy team:

Start with a Regrowth Pendant

Mercs/Tabi
Force of Nature
Sunfire
Randuin's Omen/2nd Sunfire

From here on, get whatever you need. Good options are Frozen Mallet, 2nd Sunfire (if you got Randuin's), Guardian Angel, Atma's, Banshee.

Regrowth pendant is a bad start item in my opinion, Doran's Shield gives health, armor and regen and leaves enough gold for a potion as well.

I don't agree with some advises there.
Shen is my main at the moment.
1. Tabi is (on my opinion) bad on him, considering his passive. Mercs are ok but, much better to take cleanse + swiftness.
2. Banshee on Shen!? Banshee gives Mana. You pay for that part, but you DONT HAVE MANA. Bad.

Three core items : Doran shield. Swiftness then AEGIS.

Most of the time, I do leviathan then. Really good with him BUT when your team doesn't make a kill.
Then :
Against magical team : take spirit visage, synergyze well with your A.
Against physical team, take randuin
Or, if balanced, stack HP with Rylais or frozen mallet. Both if the game is long.

Thanks people

Shen is a tank. Like all tanks: you need to focus your defense (which a tank is for) into armor, mag def, disable resist or shields that a hero has.

So, if you play against an ashe that is taking midlane: go armor. If they have a ton of stuns: banshee's veil, maybe even Quicksilver Sash (underused item i think, is cleanse + 48 mag res). When you play Shen against a mixed team, AP could work, since it boosts his shield, but then I'd suggest taking Zonya's Ring (hardcore AP) and rest armor + mag def, since the shield can only take so much anyways.

I play build my shen like this:
+boots and health pot\
+Heart of Gold
+Merc Threads
+Phage
+Frozen Mallet or Rulai(most people say Mallet but Rulai is also nice, + you gain chaser abilities spamming Vorpal Slow, and 80 points to Ulti's shield is very very nice)
+Randuin
+Guadian Angel

A long game usualy ends with two Randuin's so you got a lot of armor and CD reduction.

Other Advice:
Take a lot of magnesium for your focus and practice your map awareness