Ideal Hand:
    1x Time Vault
    1x Sol Ring
    1x Voltaic Key
    1x Island
    1x Amulet of Vigor
    2 other cards

Turn 1: Play an Island, Tap to play a Sol Ring, tap to cast Amulet of Vigor and Voltaic Key.

Turn 2: Tap Sol Ring to play Time Vault. Because of our Amulet of Vigor, it doesn't enter tapped, and we can tap Time Vault for another turn. Before you end your turn, tap your Island to pay to Voltaic Key to untap Time Vault. End your turn, take your extra one, then tap Time Vault, pay for Voltaic Key, untap Time Vault, do what you want with the remaining mana, end your turn, then repeat.


Slower Infinite Turn Combo

1x Time Vault
1x Voltaic Key
A way to get 2+ mana (2 Islands, 1 Island, 1 Sol Ring)

Play Time Vault, and Voltaic Key, then tap an Island for Voltaic Key, Untap Time Vault, take extra turn, repeat.



Other Infinite Turn Combo

1x Time Vault
1x Voltaic Servant
Mana to pay for them both.

Use Voltaic Servant's ability to untap Time Vault. Then do it again during your extra turn. Then do it again during your extra turn. Then do it again during your extra turn. Then do it again during your extra turn. Then...