I would like to start by saying i have played singed for the majority of my time on this game. I used to use this mainly on TT, but now i'm playing a lot more SR and realizing that it makes singed quite strong for that map too.

Masteries, Summoner spells, and runes
The masteries for singed are very versatile depending on the type of singed you want to play. the numbers i usually stick with are 0/9/21. I can also say that a full caster set of 9/0/21 works, and so does a tanky 0/21/9.

As for summoner spells ghost is a necessity. For the other i think there are a few viable choices. I usually use cleanse. If the other team has large amounts of CC cleanse is a great choice. And flash is nice at early levels if the other team is overconfident you can get some flash tosses in. Clairvoyance is always nice to have so if no one else gets it you should consider it. And in 5v5 i take teleport frequently. besides that i don't see others that look too good for singed.

As for the runes i run magic pen reds, mp/5 per level yellows, mana blues, and movement speed quints.
I feel like the reds blues and quints are pretty solid, the yellows could be changed out as they aren't needed though

skilling order
The skilling order on singed is situational from level one. If you are going to try a level one gank get fling, if you just want early xp and gold get poison. Then as the game progresses i prioritize R>Q>E>W usually, but if you don't randuin's which i talk about later you may want more in w earlier. Also if your team is having trouble with the other team escaping you may want more in w early. All the changes on e is the damage which is nice but its more important to keep them where your team can kill them. Pretty much learn to judge what is best for ensuring your team kills.

Items
As for items i usually start with a sapphire crystal and health pots, if they are a harass heavy team you can pick up a regrowth pennant first but i don't reccommend it. Then after i get catalyst i will buy boots. if they have little CC boots of swiftness are nice, but alot of times merc's treads are almost mandatory. After this the build starts to become situational. I usually play a tankier singed and start to build survivability. Frozen heart is my favorite armor item to buy but some prefer randuins. If i need magic resist i will buy a force of nature or a banshee's, After this if i am tanking fine i will look to buy more AP I usually go with Rylai's and sometimes abyssal depending on my own team composition. If i need to be tankier i will pick up one of the items i listed before, or a sunfire cape. These are my item suggestions, but most importantly i can say that the best is to learn what you need to have in the situation and the build that will make you most effective with your playstyle.

Playstyle
Singed is a hit and run tanky mage that provides a lot of utility for a team. he can help babysit and also get your carries fed. He is my favorite and the most fun champion that i have played to date, i recommend to everyone to at least give him a try. He is a very balanced champion so i feel i can safely say that he won't be getting any majors nerfs or buffs soon.