  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: nu-antinu, b-bbar, tau-taubar, c-cbar, light
quarks, ZZ, W^+W^-. We present the appropriate formalism for computing the
combined effect of oscillations, absorptions, nu_tau-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.
