  The rules to construct Lagrangian formulation for $\theta$-superfield theory
of fields ($\theta$-STF) are introduced and considered on the whole in the
framework of new superfield quantization method for general gauge theories.
Algebraic, group-theoretic and analytic description aspects for supervariables
over (Grassmann) algebras containing anticommuting generating element $\theta$
and interpreted further in particular as an "odd" time are examined.
Superfunction $S_{L}(\theta)$, its global symmetries are defined on the
extended space $T_{odd}{\cal M}_{cl} \times \{\theta\}$ parameterized by
superfields ${\cal A}^{\imath}(\theta), \frac{d{{\cal
A}}^{\imath}(\theta)}{d\theta \phantom{xxx}}, \theta$. Extremality properties
of superfunctional $Z[{\cal A}]=\int d\theta S_{L}(\theta)$ and ones of
corresponding Euler-Lagrange equations are analyzed. The direct and inverse
problems of zero locus reduction for extended (anti)symplectic manifolds over
${\cal M}_{min}$ = $\{({\cal A}^{\imath}(\theta), C^{\alpha}(\theta))\}$, with
(odd) even brackets, corresponding to initial $\theta$-superfield models are
employed to construct iteratively the new interconnected models both embedded
into manifolds above with reduced brackets and enlarging them with continued
ones. Component (on $\theta$) formulation for $\theta$-STF variables and
operations is produced providing the connection with standard gauge field
theory. Realization of $\theta$-STF constructions is demonstrated on models of
scalar, spinor, vector superfields which are used to formulate the
$\theta$-superfield model with abelian two-parametric gauge supergroup.
