This is my Singed guide. The way I play singed is to get as tanky as possible and harass. Once poison trail is around level 3 you can farm entire lanes very easily. Try to turn off your poison trail as soon as you can that way you don't waste your mana because you will have issues until you complete your catalyst. If you feel like you want the rod of ages first before the boots or if you want to complete the boots of swiftness before the rod of ages it depends on what you think you need more in the game.
Fight against a champ. always have your poison trail on and once your fling gets off cd us it. If you are alone just try to fling them into your poison then drop the mega adhesive so they are slowed through the poison. If you feel the need to chase someone down near a turret because of the low health after one rod of ages this is very easy(With 3/4 or full hp), just use your insanity potion, then ghost. You move absurdly fast you can turn you poison trail on then run in and fling them once. They will usually try to chase you a bit and you can pull off a kill. If you are chasing someone use a mega adhesive so you can catch up to them and fling them into poison. I almost never auto attack unless for a last hit because the poison does much more damage.
Late game you if you have your Ult you can just run circles around their champions in a team fight and keep in mind that your other two skills are very useful for saving your teammates.
Turret killing: you are very tanky and your ult is also very good at killing turrets with a wave of minions. even if there is an enemy champ hitting you just keep your poison off and target the turret. Use a heal if needed and pop ghost to make a clean getaway( with the poison trail on of course.)

Any comments would be appreciated Thanks for reading.
WibbzEX