We present a simple and powerful method for extrapolating finite-volum
e Monte Carlo data to infinite volume, based on finite-size-scaling th
eory. We discuss carefully its systematic and statistical errors, and
we illustrate it using three examples: the two-dimensional three-state
Potts antiferromagnet on the square lattice, and the two-dimensional
O(3) and O(infinity) sigma-models. in favorable cases it is possible t
o obtain reliable extrapolations (errors of a few percent) even when t
he correlation length is 1000 times larger than the lattice.