I'm rather bad at this too. Here's what has helped me in the past.

Consider the projection of this surface onto the xy, yz, and xz planes.

For the xy plane, set z = 0:

This is a hyperbola with an axis of symmetry along the y-axis and vertices at .

For the yz plane set x = 0:

This is a hyperbola with an axis of symmetry along the y-axis and vertices at .

For the xz plane, set y = 0:

This is a hyperbola with an axis of symmetry along the x-axis and vertices at .

Now the challenge is trying to put this together in 3D. That I can't help you with, but you should have at least a rough idea of what's going on.

-Dan