  The double exchange (DE) model is systematically applied for studying the
coupling between ferroelectric (FE) and magnetic orders in several prototypical
types of multiferroic manganites. The model was constructed for the
magnetically active Mn $3d$ bands in the basis of Wannier functions and include
the effect of screened on-site Coulomb interactions. The essence of our
approach for the FE polarization is to use the Berry phase theory, formulated
in terms of occupied Wannier functions, and to evaluate the asymmetric
spin-dependent change of these functions in the framework of the DE model. This
enables us to quantify the effect of the magnetic symmetry breaking and derive
several useful expressions for the electronic polarization ${\bf P}$, depending
on the relative directions of spins. The proposed theory is applied to the
solution of three major problems: (i) The magnetic-state dependence of ${\bf
P}$ in hexagonal manganites; (ii) The microscopic relationship between canted
ferromagnetism and ${\bf P}$ in monoclinic BiMnO$_3$; (iii) The origin of FE
activity in orthorhombic manganites. We show that for an arbitrary noncollinear
magnetic structure, propagating along the orthorhombic $\boldsymbol{b}$ axis
and antiferromagnetically coupled $\boldsymbol{c}$, ${\bf P}$ can be obtained
by scaling the one of the E-phase with the prefactor depending only on the
relative directions of spins and being the measure of the spin inhomogeneity.
This picture works equally well for the twofold (HoMnO$_3$) and fourfold
(TbMnO$_3$) periodic manganites. The basic difference is that the twofold
periodic magnetic structure is strongly inhomogeneous, that leads to large
${\bf P}$. On the contrary, the fourfold periodic magnetic structure can be
viewed as a moderately distorted homogeneous spin spiral, which corresponds to
weaker ${\bf P}$.
