To start things off, I play great as Singed. When I first bought him, I was using a ****ty LoL Wikia build for him, and it just didn't seem right. I then tried out EvilDice's build, and it was a total blessing. Since then, I've been doing great with Singed, and experimenting with builds for him. The core build I provided is one I've been using recently, and it does very well. Singed is fairly difficult to get used to apparently, so you might want to practice a little bit. Or at least try this build in Co-Op first. I'll provide some tips on how to actually use him properly.

Late game, you're going to piss a lot of people off with Rylai's.

Dude, EvilDice, I love your build so much bro.

Passive: Empowered Bulwark - Increases Singed's health by .25 for each mana point he has.
This passive is really cool, but if you focus too much on stacking mana only, you're going to get laughed at.

Q: Poison Trail - Toggle: Singed lays a poisonous trail which deals 22 / 34 / 46 / 58 / 70 (+30% of ability power) magic damage per second.
See this **** right here? This is your bread and butter. It harasses pushy enemies, it farms, and it lures. Toggle this on whenever you're attacking, being chased, or when you're in a team fight. Top priority for people who favor farming.

W: Mega Adhesive - Singed throws a vial of mega adhesive on the ground causing all enemies who touch it to be slowed by 35 / 45 / 55 / 65 / 75% for 5 seconds.
This ability is extremely beneficial in teamfights. It's not as important early game since less kills and teamfights go on. I love using this to ready myself for a Fling initiation. You can also help a squishy run away, or help your team catch an enemy. Using it to chase off someone chasing YOU isn't really advised unless it gets dire. You can stave them off with Poison Trail still.

E: Fling - Singed flings an enemy over his shoulder, dealing 100 / 150 / 200 / 250 / 300 (+100% of ability power) magic damage and slowing the enemy when they land.
This is another amazing ability added to Singed's arsenal. One of my favorite initiators. Does decent damage, and flings the enemy back to let a carry lay waste to them. You can also use it to fling an enemy away from your general direction if a teammate needs to escape. This is perfect for ganking. I would advise you not to use this on a fed Morde with full health, or a Mundo stacking Spirit Visage. For completely obvious reasons. You can also use this early-mid game to throw a pesky pusher into a tower's range of fire.

Ultimate: Insanity Potion - Singed drinks a potent brew of chemicals, granting him 35 / 50 / 65 enhanced damage, attack speed %, ability power, armor, movement speed, and regeneration per 5 for 25 seconds.
The superbuff. Use this in teamfights, use this to escape, use this to initiate. It's not hard to figure out when it's needed.

--Skill Combo--

Ghost+Goo+Fling+Poison Trail
This is a great combo to initiate with. Goo to slow enemy, Ghost to speed up, Fling to do damage and initiate, Poison trail for gradual damage. If they try to run back, go before they do so they have to run through your trail. At that point, your Fling is probably back up, you you can rinse repeat Fling.

IN THE BEGINNING.....
You could either start with Saphire Crystal +Health and Mana Pots for the extra mana (Singed has ****ty mana early game); Or you could start with Boots of Speed, and get 1 Health + 2 mana.

Mid Game
You might want to get Boots of Swiftness, you know, for no reason, since Singed already doesn't depend on the ability to run and Fling an enemy. He has amazing starting speed.
RoA is Singeds bread and butter. Banshee's veil is quite amazing as well. Have you seen a successful Singed without Rod? Exactly.

Late Game
So I usually go with Randuins. I go with Rylai if I can afford it, if not, I replace it with FoN. However, having Rylai's gives you an amazing payload. SLOWING poison trail. This'll make teamfights a complete breeze. Once you get your Rand and Ry built, the last is up to you. I usually go with Guardian Angel.

USE THESE

Ghost - YES, ALWAYS USE GHOST
Cleanse - Not going to lie, it's very helpful. This spell has saved me from numerous ganks.
Teleport - This will be super helpful so you can be the star of any teamfight going on.
Flash - If you wanted to be a real ****, you could Flash+Fling. Calls for some laughs.

I'll work on this, make it nicer etc.
Maybe when I'm not drunk.