We study the fluxes of neutrinos from annihilations of dark matter particles in the Sun and the Earth. We give the spectra of all neutrino flavors for the main known annihilation channels: νν¯, bb¯, ττ¯, cc¯, light quarks, ZZ, W⁺W⁻. We present the appropriate formalism for computing the combined effect of oscillations, absorptions, ν_τ-regeneration. Total rates are modified by an O(0.1–10) factor, comparable to astrophysical uncertainties, that instead negligibly affect the spectra. We then calculate different signal topologies in neutrino telescopes: through-going muons, contained muons, showers, and study their capabilities to discriminate a dark matter signal from backgrounds. We finally discuss how measuring the neutrino spectra can allow to reconstruct the fundamental properties of the dark matter: its mass and its annihilation branching ratios.