Dark matter (DM) is one of the major components in the Universe. However, at present its existence is still only inferred through indirect astronomical observations. DM particles can annihilate or decay, producing final-state Standard Model pairs that subsequently annihilate into high-energy $\gamma$-rays. The dwarf spheroidal galaxies (dSphs) in the Milky Way DM halo have long been considered optimal targets to search for annihilating DM signatures in GeV-to-TeV $\gamma$-ray spectra due to their high DM densities (hence high astrophysical factors), as well as the expected absence of intrinsic $\gamma$-ray emission of astrophysical origin. For such targets, it is important to compute the amount of DM in their halos in a consistent way to optimize the $\gamma$-ray data analysis. Such estimates directly affect the observability of DM signals in dSphs, as well as the DM constraints that can be derived in case of null detection. In this contribution, we present the results on the sensitivity of the Cherenkov Telescope Array (CTA) for DM annihilation and decay searches using planned observations of the Milky Way dSphs. We select the most promising targets among all presently known dwarf satellites, providing new determinations of their expected DM signal. This study shows an improvement of approximately an order of magnitude in sensitivity compared to current searches in similar targets. We also discuss the results in terms of cuspy and cored DM models, and investigate the sensitivity obtained by the combination of observations from different dSphs. Finally, we explore the optimal strategies for CTA observations of dSphs.