Well first of all, I don't usually make any guides, but I've been playing this way (or similar) for quite some time I've done really well almost everytime.

Singed gets a bonus on health for all the mana that he has. This build will use that to it's advantage.

This build is all about movement speed and loads of health.

This build is best for fighting against close combat champions.

~ Try to get infront of enemy champions who are running away, that way they take damage from Poison Trail. You can also do this so that they don't keep running forward, and change paths hopefully into an ambush by your teammates
~ Fling enemies into your tower or your team if they are running away
~ At the start of the game, use Poison Trail sparingly, it will drain your mana pretty fast
~ Try to poison all of the minions by running through and around them, or run a bit ahead of them so they take damage and don't damage you

I usually go with runes that give mana, magic pen, or movement speed, since mostly what I do as singed is run around with 'q' active.

I usually always have teleport for emergencies (them attacking your tower). Other then that, pick which one you are best with.

I usually stick with these items but sometimes switch them depending on the situation. I always get Rod of Ages first and follow with Boots of Swiftness. You want to try to get Rod of Ages as soon as possible. I usually get it around 12 minutes in.

Get a Tear of the Goddess next, that way you can start using spells to increase your mana. Remember Mana = More Health + Longer Poison Trail. If you upgrade it to Archangel's Staff then you won't need to worry about ever running out of mana, you can practically leave Poison Trail on.

The Next items are where it depends on the opponents. Rylai's crystal scepter will make sure no one catches you with it's slow, as well as increase the damage on poison trail and give you more health.

Depending on whether you are fighting a more magic based or attacked based team decides whether to get Banshee's Veil or Frozen Heart first. If they are very heavy attack damage, you may want to get thornmail instead.

It is really easy to get lots of money from assists as singed just from your poison trail.