Describe the hybrid orbitals used by the central atom and the types of bonds formed in o3

Hybridization in ozone, O3 

...O = O 1 lone pair on central O, 2 lone pairs on terminal O 
../ 
O 3 lone pairs on terminal O 

I didn't show the second of two resonance structures in which the single and double bonds are reversed. In reality, both bonds are identical have a bond order of 1.5 due to delocalized pi-bonding. 

The central atom exhibits sp2 hybridization since there is trigonal planar electron pair geometry. The notion of hybrid orbitals was "invented" by Linus Pauling in the 1930's as a way of explaining the geometry of molecules, primarily the geometry of carbon compounds. 

If the electron pair geometry is linear, the hybridization is sp. 
If the electron pair geometry is trigonal planar, the hybridization is sp2. 
If the electron pair geometry is tetrahedral, the hybridization is sp3. 

The notion that there is sp3d and sp3d2 because of d-orbital participation has been debunked. Chemists know today that there is no d-orbital involvement in hypervalent molecules regardless of what some out-of-date textbooks and some teachers' dusty old notes may say. Instead, the best explanation involves 3-center, 4-electron bonding.