Polarization induced by cosmological scalar perturbations leads to a typical anisotropy pattern, which can best be analyzed in a Fourier domain. This allows one to distinguish a cosmological signal of polarization unambiguously from other foregrounds and systematics, as well as from polarization induced by nonscalar perturbations. The precision with which polarization and cross-correlation power spectra can be determined is limited by cosmic variance, noise, and foreground residuals. The choice of estimator can significantly improve our capability of extracting a cosmological signal, and in the noise-dominated limit the optimal power spectrum estimator reduces the variance by a factor of 2 compared to the simplest estimator. If foreground residuals are important, then a different estimator can be used, which eliminates systematic effects from foregrounds so that no further foreground subtraction is needed. A particular combination of Stokes Q and U parameters vanishes for scalar-induced polarization, thereby allowing a direct determination of tensor modes. Theoretical predictions of polarization in standard models show that one typically expects a signal at the level of 5-10 μK on small angular scales and around 1 μK on large scales (l < 200). Satellite missions should be able to reach sensitivities needed for an unambiguous detection of polarization, which would help to break the degeneracies in the determination of some of the cosmological parameters.