I want to start off by saying this is my first guide ever. I decided to make an ap singed build that wasn't just your standard RoA build. Almost all of the other singed guides on this site are for building an off-tank singed, which is best if you have no other tanks, but if you do have another tank on your team i find it best to be able to do the most damage with your fling/run away with poison combo. Singed also has good ap ratios on fling and poison trail. The ap ratio on poison trail may look small but when you factor in that the poison continues to deal damage for 5 seconds after they leave it, effectively making its ap ratio greater than 1.

Pros:
Singed has the best self-buff ability in the game
Poison Trail does a lot more damage than it seems
Excellent initiator with his fling ability
Great chaser/kiter
Excellent pusher

Cons:
No damaging ranged spells
Not very good physical damage when ult isn't active
Very prone to cc effects with this build

As far as summoner spells, I find Ghost is a must on Singed. This is mostly because the movement speed bonus will allow you to fling pretty much whoever you want, as well as escape a possible gank. Another reason I enjoy ghost on Singed is when your chasing an enemy and fling is on cooldown, I find it much more effective to just keep running ahead of enemies with poison on instead of auto-attacking.

I don't think that there is a definitive second spell for Singed, so it's all about your preference. I usually take Ignite in case the enemy team has good healing as well as possible last hitting fleeing champs. Cleanse is another good choice for Singed as he is prone to cc while trying to fling enemies in team fights. The only spell i wouldn't take is Clarity because you should never run out of mana after level 12 or so.

As far as runes go I like Greater Mark of Magic Penetration for magic penetration, and greater seal of replenishment for mana regen. I also like to have some Greater Glyph of Magic Resist to provide some MR. For the quints I prefer Greater Quintessence of Movement Speed becasue movement speed is essential for Singed but I also find that the Greater Quintessence of Health is good for almost any champ, and Singed is no exception.

Empowered Bulwark: Most of the guides I see build to generate as much from this ability as possible. I tried that and found that I wasn't doing nearly enough damage. I also find that too much mana is just a waste of gold. There are much better passive abilities than this.

Poison Trail: My favorite ability in the entire game. Use it to farm, kite, and deal heavy damage. Many players I've seen greatly underestimate the damage this ability does, especially in an AP/magic pen build like this one. I've gotten many double and triple kills just by running away from over pursuing enemies. Max this ability first. It makes you one of the most dangerous level 9-11 killer in the game.

Mega Adhesive: This ability is best used for escaping enemies and helping your team escape. It is also fairly useful for catching an unwilling target to fling back into your team. I take my first rank at level 4 and max this right after poison trail. The reason for this is that fling doesn't do a whole lot of base damage anyway and its cooldown doesn't change, so I find that having the extra slow percentage much more useful than extra fling damage.

Fling: Your fight initiator and potential ally saver. Use it to throw the enemies support or carry into your team and watch them die. Use it to toss enemy champs away from dying allies. Of course make sure your poison trail is active before flinging. Learning when to fling and when not to is the whole key to playing Singed. I take one rank at level one to kill careless over-pushers during laning, but dont level it up the rest of the way until I have to.

Insanity Potion: As I said before...the best self-buff in the game imo. It increases all of the offensive stats you can think of. Great for pushing, chasing and the extra ap it adds to poison trail is really nice. It also lasts longer than any other buff and has a fairly short cooldown. The cooldown starts as soon as you activate it too which I enjoy very much. Like most ults, level this up every chance you get.

I always start with a Sapphire Crystal and 2 Health Potions. Then i start working on boots. My personal preference is for Sorcerer's Shoes for the magic penetration, seeing as about 75% Singed's damage is magic. Other goods choices are Boots of Swiftness, for more speed, and Mercury's Treads if the enemy team has lots of cc. I also take this time to buy a few Mana Potions, it should be last time you need to. After that I finish up my Rod of Ages and start working on either the Void Staff or Will of the Ancients. The will of the ancients allows you to heal while dealing considerable damage to enemy chasers. The void staff is there for AP and magic penetration, plain and simple. Magic penetration is the key to this build as enemies generally don't realize just how much damage Poison Trail is doing until it's too late. Now the game usually ends before I finish the void staff but if it still goes on I like Rabadon's Deathcap and Lich Bane. Rabadon's obviously for the huge increase in ap and lich bane for the movement speed, ap and the extra damage on your next attack after Flinging an enemy. You will always get at least one auto-attack in after flinging someone, and when your Insanity Potion is active you will have over 500 AP by this point in the game, making you much more dangerous late game. If you still would prefer to have some magic resistance I find the Abyssal Mask can make a good substitute for the void staff.

Early Game: The hardest part about playing Singed is his early game. He is easy to harass and does low fairly low damage for a melee attacker. Don't push too far early game because you are prone to harassing and ganks early. Having a high damage teammate laning with you allows you to be aggressive and will lead to getting first blood a lot. Singed is also a great tower hugger with his fling ability. I only use poison is small spurts to help with minion last hitting, otherwise the only time i have it on is running away or right before a fling attempt. I rarely oom early game by saving poison and mega adhesive for really good killing opportunities or saving my teammates.

Mid Game: About now your poison should be maxed out and you should have enough mana to use poison trail in every combat situation (including farming) without running out. This is the part of the game where Singed excels. The majority of my kills come between levels 7 and 13. Just farm, push, help your team fight, whatever is called for at that moment. Singed's versatility is great from here on out. He's great at backdooring with his posion, ult and escapability. Just remember that you aren't actually a tanky tank, this build sacrifices toughness for damage. It is Singed's job to be a jerk. Grab someone, run away and let your poison trail do the work. Singed is also a good baiter, just dangle yourself out in front and draw them in...the poison trail should damage all chasers enough to give your team a significant edge when the enemy over pursues.

Late Game: Singed plays pretty similarly late game as he does mid. Usually if my team is fed I will backdoor other lanes, if not I stay with them and help initiate, hopefully by flinging their carry or support. With your heavy AP, team spell vamp and magic penetration your poison will do heavy damage and give you an edge in all fights.

That's it for my Singed build. Hope you give it a try. Any ideas for improvement are greatly appreciated. It does play quite differently late game than your standard off-tank build and may take some getting used to, but if you've had a good game so far they will want to start focusing you which will allow your carry to wreak havoc while you kite them to death. Sit back, relax and have a drink. (Shaken, not stirred of course)