  We develop a superfield formulation of gauge and matter field theories on a
two-dimensional sphere with rigid N=(2,2) as well as extended supersymmetry.
The construction is based on a supercoset SU(2|1)/[U(1) x U(1)] containing
$S^2$ as the bosonic subspace. We derive an explicit form of supervielbein and
covariant derivatives on this coset, and use them to construct classical
superfield actions for gauge and matter supermultiplets in this
superbackground. We then apply superfield methods for computing one-loop
partition functions of these theories and demonstrate how the localization
technique works directly in the superspace.
