What is the truth table for double turnstile? From what I understand α |= β means that if α comes out true, so does β. ie, α entails β. This got me thinking, I know that there are truth tables for α → β, α ∨ β, etc. Is there a standard truth table for α |= β?

Your understanding is correct: $α \vDash β$ means that $α$ is a logical consequence of $β$.

There is no "standard" truth table for it, but of course you can use truth table: write a t-t for the formulas $α$ and $β$ and check if in every line of the t-t where $α$ is evaluated to TRUE also $β$ is TRUE.

If so, this will show that the second is consequence of the first.