I will guide you and explain how to play Singed my way. This usually leads to the opponent wanting to smash his/her computer into pieces. Singed is my personal favorite tank. (Ive gotten a few pentas with this build). I focus mainly on TANK items, not mage. This is what makes it so much fun :)

For masteries I go 0/21/9.

6 Magic res, 6 armor, nimbleness, veteran, cleanse and of course the 4% reduction. Now you can either chose to go 9/21/0, grabing the cdr and magic pen. Thats a free choise, however i got with advanced ghost and greed + exp.

For runes there are:

REDS: Magic Pen / Magic res/ Armor
BLUES: Mana reg/ AP (however kind of unnecessary)/ Magic res (Flat or /lvl)
YELLOWS: Armos/Health/Magic res/ Mana reg
QUINTS: Health/Movement/

(whatever you prefer)

Summoner spells:

Recommended from me:

Ghost: is a VERY good choise for Singed. You'll notice while playing. Perfect hunting/escaping, combined with ult = fcking rabbit.

Cleanse: Also a good choise. Stuns and snares/silences are extremely annoying to someone like Singed.

Teleport: Also good choise, especially when soloing. I will make a Solo guide later on, ill explain that part then. Anyways teleport is awesome in combination with Singed's farming ability.

Exhaust: A pretty decent choise. Works well with poison, fling, escape and hunt.

Flash: CAN be good for fling/escape. I however choose Ghost over this one when playing Singed.
Clarity: ONLY if youre playing with a manahog teammate.

Revive: Wont need.
Ignite: Youre not gonna focus on Kills. Not really needed.
Heal: Wont need.
Rally: No.

CV: Depends. I would not choose this one, but if your team is stupid enough to not have this one, yet having a support that for some reason wont buy wards.. okay. Otherwise No.

Smite: There is a way to jungle with Singed.. however jungle Singed needs perfect teamspeak and quite advanced playing.

Fortify: You CAN pick fortify. It does help. Allthough dont be afraid to use it. Ive seen Singeds playing with Fortify and using it ONCE /40 min.

Okay this is the part when you get to test your skill.
Core
[*] Boots of Swiftness OR Tabi OR Mercury Treads (your ult is covering this part a bit though) Depending on what you're facing. I however go Swiftness 90% of every match.
[*] Rod of Ages: This is a Must-Have item. You get AP, Health AND Mana. Mana also converts to a bit of health which makes this item even better.
[*] Randuim's Omen: And here's my favorite. Provides Health, Armor, chance of slow, ACTIVE AoE Slow and regen. The active is insane.

Okay. Begin with boots and 2 health potions + a mana potion. Some choose to go 3 health potions, but you will find out that Singed does consume a lot of mana, making a mana potion more beneficial.
Try to stay in lane until you have about 1.3k gold, which is when you teleport back and get your Catalyst. This item provides a better survive abillity as well as a chunk of mana PLUS a great passive. If enemy team has a jungler: keep in mind to buy wards! Also buy some potions if necessary. Depending on what you're facing your next item will be:

Heavy AD: Wardens Mail and try to get a Randuim / thornmail. I however prefer Randuim.
Heavy AP: Heart of gold + Negatron and try to get a Force of Nature OR Banshees. Force of nature in case of nuke, Banshee in case of lots of cc. NOTE: If you go mercury treads, banshee wont be AS necessry. The second passive is covered by Rod of Ages.

If youre getting fed, get a little of everything. Boots, RoA, Heart of Gold, Warden, Negatron etc.. whatever is necessary. The purchases however shows a big defference between unskilled - skilled.

You can replace FoN (early/mid game) with quicksilver. If they have morde with ult/ lots of blinds, cc heavy.

For the Last items (Guardian angel, Sunfire) : These are optional. I do recomend them though. You can also try to switch Rod of Ages for Rylais if youre feeling for it (it gives slow on poison which is freaking awesome!). Rod of ages is still strongly recommended (gives mana as well, not only ap and hp)

PROS:
[*] When youve Got your four items YOU ARE ANNOYING AS FCK and ALMOST IMMORTAL.
[*] Annoying slow
[*] Good target ability
[*] Ult and you become extremely hard to take down
[*] Poison is VERY underrated. Ive got Penta with Singed two or three times cause of ignorance of the Poison
[*] Extremely hard to chase down / Good at Chasing
[*] Awesome overall Tank.

CONS:
[*] Mana problem early/mid. (You have to learn mana usage by heart..)
[*] Itemspurchases is something you have to learn yourself. Keep in mind that Health is usually better than armor/magic res early/mid.
[*] Lack of Stun
[*] Only one CC

Okay you can either put first point in Poison or Fling. I want to get up poison early and since i'm playing ranked, no one is stupid enough to go near turrets for early fling kill.. Fling is also a good choise if your laningmate is burst dmg (panth, poppy) raw dmg (trynda,olaf) or even ap nuke. Its also perfect for saving your *** or your mate's. Why I chose to put poison at lvl 1 is cause I want to max it as fast as possible. The damage later on is insane. Why i dont lvl fling more than once, is cause you're only increasing dmg AND mana cost while you instead, could have upped MA (your W). I then choose to kind of pick equally Q/W, since both provide slightly better stats/ level. Your W becomes SO frustrating at later lvls.
Fling enemies when youre lanemate is in danger/when youre hunting. You can fling enemies into turrets and get easy kills, however ranked players arent that stupid to actually allow you to do it.

And of course, Your ULT. It's insane (even after nerf). Gives you Mana regen, Health regen, Magic Res, Movement speed (this combined with ghost is ****ing SCARY) and AP. Use this when Engaging a teamfight.

When entering a teamfight pop your ult, run into them, absorb their ults and press randuim (i always keep randuim at the second item slot, since "2" is right above the "W" on the keyboard) and pick the easiest target to fling (OR if they have a kat, save fling for her), by easiest i mean the most squishy (often Ad/ap carrys that dont bother buying hp until later) such as Kennen, Teemo etc. W the ones that go for the carry in your team. Or the ones that try to escape. Keep Poison trail active all the time, and use cleanse if needed.

NOTE: Try to make them chase YOU. This is Called Toxic Angel. You rush in, poison, fling, randuim, ult, ghost and Run around, try to make them focus you. You ult and FoN covers the health. Low on health is a Perfect taunt. While they chase you, your team is free to ambush them. Cast W if you want, just to be annoying or actually to save yourself.

If they however have a powerful and fed nuke + cc, be carefull using this.

At late game, it wont be necessary to even think. Just do it. Your a fcking demi god with about 4k health, chunk of magic res, chunk of armor, extreme reg and good cc. THIS is when your opponent want to break their computers in to half. And there's nothing we love more, is there? :)

Singed works well with AD (Trynda, Gp, BURTSERS) AP (Morgana, Veigar, Gragas. Nukers in general.) and Solo. You can also Jungle but as mentioned, needs understanding of Singed.

You are of course free to change what you want. I prefer this way of playing. Feel free to comment/rate. This is my first Guide so every feedback is wellcome :)