Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
To start off i usually take Fling and buy a mana stone. It will help you lane longer and give you more health and mana. Just stay back and try to last-hit some minions and if an enemy champion comes far enough from their turret and is weak or you have a frisky teammate you can ghost and fling to try and get a cheap first blood. Other than that just try to last hit and level your poison trail to kill as many creeps as possible. Around level 6 you can start really harassing enemy champs. First trip back to the store i usually get my boots and then try to get a catalyst early. Then work on finishing you RoA and either Mercury's Treads or Ninja Tabi (Really just depending on the enemy team. I usually go with the Mercury's Treads for the magic resist and it helps chase enemies too, but for melee-heavy teams i'll sometimes go with the Ninja Tabi)
Mid game is basically just pushing towers. You can really help with ganks and friendly champion AoE spells with your fling and your teammates will love you. And your ulti will really help you get kills with the boost to attack, ap, and movement speed. For the mid-game item build i always grab a banshees veil first because it gives you health, mana (with Singed's passive ability that means even MORE health), and a good deal of magic resist. Then i get a frozen heart for the Mana (health) and Armor. The Cooldown reduction helps with your ulti but is not a necessity for this build.
Late game you'll have enough health, armor, and magic resist to stay alive and any type of gank where you might die you can always cleanse/ghost your way out of. If needed you can always use your ulti if you absolutely have to for the movement speed and health regen bonuses. Again, depending on the team is how you decide which item to get first. Against a caster-heavy team it's definitely smart to get a Force of Nature. Against teams that are mostly melee I would go with a Randuins omen. Then buy the other if you have enough time to finish the build before you win.