Cast Switcheroo by paying ({4} magic symbol) ({U} magic symbol) , giving control of Vilis to an opponent, and giving you control of a creature that opponent controls.
During that opponent's draw step, they draw a card.
Nekusar triggers, dealing 1 damage to the opponent.
Vilis triggers, causing the opponent to draw a card.
Repeat from step 3 until the opponent loses the game either due to drawing from an empty library, or from having 0 life.