Poison Trail is very effective for farming and harassing, allowing Singed to dominate his lane. Poisoning the opposing minions as they advance is an effective strategy for farming lanes.
A good strategy for farming is to push your minions to the enemy turret, then run past it to poison the next wave as it comes. However, this puts you behind the enemy tower, so be wary of ganks.
When facing melee champions, you are capable of zoning them by poisoning the area near your own minions so their farming capabilities are hindered severely.
Turn off Poison Trail when unnecessary as it drains mana quickly.
Poison Trail goes invisible to opponents when you enter brush. It is also possible to create a very faint poison cloud by quickly double tapping your Poison Trail.
While being chased, if you can afford to run in a zig-zag pattern, do so to make sure your opponents will be poisoned at least once.
Mega Adhesive is one of the best slows in the game, and it should have at least one rank before level 5. The upper ranks simply increase the slow percentage. A well-played Singed can lead a target with the glue, catch up to the target, then Fling him back in to the glue for maximum effect. This may take some practice, as all ranks have only a 5 second duration.
Fling is your most versatile ability and can be used to toss enemies into your turret, isolate them from their teammates to set up an allied ambush, and save lives by tossing enemies away from weak or fleeing allies. Be sure to use it at the extent of its range, the further you are from a target when you Fling it, the further they will get tossed behind you.
Near thin walls, this can be used to throw an enemy across, repositioning them in an unfavorable location.
Insanity Potion is useful for chasing enemies and is a useful asset in any major team battle for its all-round bonuses. It has an incredibly short cooldown considering its bonuses, so don't worry about wasting it to run away from a gank gone wrong. Its short cooldown also means it can be used in lane to simply regenerate mana and hp.
Using Fling to throw an enemy into your Poison Trail is a very simple but an effective harassment combo.
Although not a caster in the true sense, Singed benefits greatly from magic penetration runes to make sure your opponents get full damage from Poison Trail. A full caster setup will allow him to deal quite heavy damage with the capability of tanking.
Consider maxing Mega Adhesive before Fling, as this spell grants you better zone control and CC with a 75% slow, instead of Fling, which grants you only 45 bonus damage per level and increases its mana cost.
Put a second point in Fling early because its damage is lower than its mana cost at Rank 1.
Fling must be used wisely when diving a turret, if you are low level and the enemy is on the side of the turret facing your base you can E + W easily to attack, however take into consideration that if you toss the enemy when he moves on the other side of the turret you could possibly land him near to the turret and take lots of damage or land him further into the enemy lane and force your ally/partner to have to walk through the jungle or make his escape easier.
When you use Fling, you can autoattack him at the same time. This is done by clicking on the enemy champion while he is in mid-air. The damage of Singed autoattack can, in early game at least, be just that little bit of damage which forces your opponent to play passive or maybe even recall.
Singed is one of the only champions who can proxy, which is running behind enemy lines to kill off their minions before they reach the person who's pushing the lane, due to Poison Trail. Lissandra can do this with her W and E skills as well.
Building mana as Singed is a good idea because of Empowered Bulwark, it is sometimes more cost effective than buying health directly because 100 gold invested in mana will also give you health worth 33 gold.
Note, however, that quickly toggling Poison Trail is the best way to gain stacks, and he will eventually have mana problems (3-5 minutes with a "blank" tear), simply by poisoning as little as possible to farm his lane. Catalyst, overall, provides more mana.
Later upgrading to a Archangel's Staff will grant quite a bit of AP. If he manages to gain enough charges he will gain a Seraph's Embrace, offering up additional durability in the shield.
Because Champion gameplay is very dependent on positioning, consider starting with Boots of Speed and picking up other speed items as you play.
An early Ancient Coin can help overcome the mana cost of Singed's abilities. Late game, this can be built into a Talisman of Ascension for additional stats/the movespeed boost. Remember to use it defensively as well as offensively, as nearby teammates will benefit from it as well.
Lich Bane is a very powerful item to increase Singed's burst damage. It allows you to deal some extra damage with your guaranteed auto attack after flinging the enemy backwards. On top of that, the extra movement speed will synergize with the flat movement speed buff from Insanity Potion and the mana will give some health with Empowered Bulwark.
Keep in mind that while chasing Singed, Poison Trail will slowly drain your health away while Insanity Potion will regenerate his health back and due to its long duration, Singed can run back and deal the finishing blow on you with Fling.