  In this paper, we first provide an explicit description of {\it all}
holomorphic discs (``disc instantons'') attached to Lagrangian torus fibers of
arbitrary compact toric manifolds, and prove their Fredholm regularity. Using
this, we compute Fukaya-Oh-Ohta-Ono's (FOOO's) obstruction (co)chains and the
Floer cohomology of Lagrangian torus fibers of Fano toric manifolds. In
particular specializing to the formal parameter $T^{2\pi} = e^{-1}$, our
computation verifies the folklore that FOOO's obstruction (co)chains correspond
to the Landau-Ginzburg superpotentials under the mirror symmetry
correspondence, and also proves the prediction made by K. Hori about the Floer
cohomology of Lagrangian torus fibers of Fano toric manifolds. The latter
states that the Floer cohomology (for the parameter value $T^{2\pi} = e^{-1}$)
of all the fibers vanish except at a finite number, the Euler characteristic of
the toric manifold, of base points in the momentum polytope that are critical
points of the superpotential of the Landau-Ginzburg mirror to the toric
manifold. In the latter cases, we also prove that the Floer cohomology of the
corresponding fiber is isomorphic to its singular cohomology.
  We also introduce a restricted version of the Floer cohomology of Lagrangian
submanifolds, which is a priori more flexible to define in general, and which
we call the {\it adapted Floer cohomology}. We then prove that the adapted
Floer cohomology of any non-singular torus fiber of Fano toric manifolds is
well-defined, invariant under the Hamiltonian isotopy and isomorphic to the
Bott-Morse Floer cohomology of the fiber.
