Identify the hydrogen ion donors and hydrogen ion acceptors for ionization of H2SO4 in water?

H2SO4 H(+) + HSO4(-)
HSO4(-) H(+) + SO4(2-)

H(+) + H2O H3O(+)

As from the above equations, Hydrogen ion donor is H2SO4 and HSO4(-).
Hydrogen ion acceptor is the water molecule H2O which forms the hydronium ion, H30(+) that makes the solution acidic. More hydrogen ions, therefore more hydronium ion hence more the acidity of the solution.

Acid - H2SO4
Its conjugate base is HSO4(-).

Acid - HSO4 (-)
Its conjugate base is SO4(2-).

Acid - H3O(+)
Its conjugate base is H2O.

This is on the basis of Bronsted-Lowry concept of acids and bases.
'Base always accepts a proton and acid tends to donate a proton.'

Hope that helped.