Not Updated For Current Season
Singed is a Champion that is build to keep moving with Poison Trial on, do not think Poison Trail is nothing, because it is the Heart of this Character.
The first thing you must need in playing Singed is patience. Items like Rod of Ages takes a lot of patience early game to get, so you must play defensively.
Singed can outmatch most champions, such as Amumu and Warwick.
As you all know Warwick is a tank destroyer and his best trait is that it can outrun half-dead champions. (A Chaser). But with Singed's Speed and his Poison Trail, he can reduce Warwick's HP under 1/2 before he even gets to you and when that happens, a Fling and a few punches will finish him off, but I personally love to run around enemy champions while they think it's fine to attack me.
Amumu on the other hand is a bit trickier. We know Amumu has his amazing burns and all but Singed's Poison does exactly the same thing, and why is Singed better? Because he has amazing HP to be able to tank Amumu's burning plus fling can keep your distance while Amumu is suffocating in your gas.
About Singed's build, most people play Singed with 2 RoA and 1 Rylai's to slow people, but we actually don't need to, and I have noticed that many other Singed build focuses on Singed playing so Defensively, with Armor and M.Resist. This build is for players who plays offensively and actually makes use of that Damage buff with Singed's Ult.
When people play Singed, they forget that when you're in Ult, your damage increases too, if you use Lichbane, once after using Fling, go in and start spamming your clicks, dealing alot of damage while your Poison Trail is burning off their HP along with you attacking, use Mega Adhesive to slow them and re-activate Lichbane's effect and attack again. (This advice is actually useless in most matches because they end after you get your Archangel's Staff.)