NASA and ESA are planning missions to directly detect and characterize terrestrial planets outside our solar system (nominally NASA-Terrestrial Planet Finder and ESA-DARWIN missions). These missions will provide our first opportunity to spectroscopically study the global characteristics of those planets, and search for signs of habitability and life. We have used spatially and spectrally-resolved models to explore the observational sensitivity to changes in atmospheric and surface properties, and the detectability of surface biosignatures, in the globally averaged spectra and light-curves of the Earth. Atmospheric signatures of Earth-size exoplanets might be detected, in a near future, by stellar occultation as well. Detectability depends on planet's size, atmospheric composition, cloud cover and stellar type. According to our simulations, Earth's land vegetation signature (red-edge) is potentially visible in the disk-averaged spectra, even with cloud cover, and when the signal is averaged over the daily time scale. Marine vegetation is far more difficult to detect. We explored also the detectability of an exo-vegetation responsible for producing a signature that is red-shifted with respect to the Earth vegetation's one.