How do we construct reductions for NP-Completeness I'm wondering in what direction we construct reductions to prove that a problem is NP-complete. Say the question is asking to prove that the vertex cover problem is NP-complete given that the independent set problem is NP-complete. 

In this case, do we start with an instance of the vertex cover problem and show how we can transform this instance into an instance of the independent set problem? Or, do we start with an instance of the independent set problem and transform it into an instance of the vertex cover problem?

I understand the relationship between vertex cover and independent set, however, I am confused on the direction of reduction.
You reduce Independent set to Vertex cover. You want to say that the vertex cover is atleast as hard as Independent set. One could way to remember is you are using a subroutine for vertex cover to solve Independent set. Since Independent set is Np-C you know you know the subroutine you used can't be polynomial. If you do the other way around using a subroutine of Independent set to solve Vertex cover. This does not say anything, as there might be a better way to solve vertex cover and does not show anything.