  We study the low-energy effective action $S_{eff}[\varphi]$ for the
one-component real scalar field theory in three Euclidean dimensions in the
symmetric phase, concentrating on its static part --- effective potential
$V_{eff}(\varphi)$. It characterizes the approach to the phase transition in
all systems that belong to the 3d Ising universality class. We compute it from
the probability distributions of the average magnetization in the 3d Ising
model in a homogeneous external field, obtained by Monte Carlo. We find that
the $\varphi^6$ term in $V_{eff}$ is important, while the higher terms can be
neglected within our statistical errors. Thus we obtain the approximate
effective action $$ S_{eff} = \int d^3 x \left\{
  {1 \over 2} \partial_\mu \varphi \partial_\mu \varphi +
  {1 \over 2} m^2 \varphi^2 + m g_4 \varphi^4 + g_6 \varphi^6 \right\} , $$
with arbitrary mass $m$ that sets the scale, and dimensionless couplings $g_4 =
0.97 \pm 0.02$ and $g_6 = 2.05 \pm 0.15$. The value of $g_4$ is consistent with
the renormalization group fixed point coupling. This $V_{eff}$, when used
instead of the traditional $a \varphi^2 + b \varphi^4$, turns the
Ginzburg--Landau description of the long-wave properties of the 3d theory near
criticality into quantitatively accurate. It is also relevant to the theory of
cosmological phase transitions.
