See photos here for images of what you would like your grape buds to look like:

As you can see, all three buds are alive, no hint of brown or black color. This is a deep cut of the bud though.  First cut shallower to expose the primary bud first (as that is the one of most interest) and then make successive cuts to show the secondary and tertiary buds.  Cutting too deep usually shows green tissue, thus possibly leading to a false positive (or negative — meaning it is green so must be alive, but only the subtending tissue is alive and the bud itself is dead).

And, not so much:

In this case the primary bud is dead, showing a black center and brown around it.  The secondary bud is alive however. The tertiary is not exposed, as a deeper cut would need to be made in order to show it.