VoronoiMesh produces a MeshRegion, so you use the mesh-related functions. If vor was your voronoi mesh could use MeshCells[vor,3] to get the 3D cells. This will give you the unnormalized polyhedra using indices as in a GraphicsComplex. To get polyhedra that can "stand alone" using actual coordinates, use MeshPrimitives[vm, 3].
So, you could select polyhedra that contain a given point using RegionMember:
Select[MeshPrimitives[vm, 3], RegionMember[#, {0, 0, 0}] &]
