What is the structure of know its hybridization as sp3d but cannot quite understand its diagram in free space,

The shape of XeO₂F₂ is Trigonal bi-pyramidal see-saw tetrahedron (see attached pictures)
- As you said the hybridization of Xe here is sp³d so its geometry has to be Trigonal bi-pyramidal in which F atom located on axial positions but for the final shape we exclude lone pair on Xe to give see-saw shape (see second picture) 
- Remember that we have 5 pairs (4 bond pairs + 1 lone pair) and we have to place lone pair at equatorial position.

C) electrons encircling a nucleus with neutrons and protons