Time Vault enters the battlefield tapped.
Time Vault doesn't untap during your untap step.
If you would begin your turn while Time Vault is tapped, you may skip that turn instead. If you do, untap Time Vault.
: Take an extra turn after this one.
10/4/2004 If multiple “extra turn” effects resolve in the same turn, take them in the reverse of the order that the effects resolved.
10/1/2008 The choice of whether or not to skip a turn is made as that turn would begin, and only if Time Vault is tapped at that time. If you choose to skip your turn, Time Vault untaps before anything else happens in the next turn.
10/1/2008 This wording means that you no longer end up skipping multiple turns if you find a way to activate the ability multiple times.