Cast First Day of Class by paying 1, causing all creatures that enter the battlefield under your control this turn to get an additional +1/+1 counter put on it.
Activate Sling-Gang Lieutenant by sacrificing Putrid Goblin.
Putrid Goblin's persist ability triggers, returning itself from your graveyard to the battlefield with a -1/-1 counter on it.
Putrid Goblin enters the battlefield, triggering First Day of Class, putting a +1/+1 counter on Putrid Goblin.
Resolve the Sling-Gang Lieutenant ability from step 2, causing an opponent to lose 1 life and you to gain 1 life.