By numerical and variational solutions of the Gross-Pitaevskii equation, we studied the localization of a noninteracting and weakly interacting Bose-Einstein condensate (BEC) in a disordered cold atom lattice and a speckle potential. In the case of a single BEC fragment, the variational analysis produced good results. For a weakly disordered potential, the localized BEC's are found to have an exponential tail as in the weak Anderson localization. We also investigated the expansion of a noninteracting BEC in these potentials. We find that the BEC will be locked in an appropriate localized state after an initial expansion and will execute breathing oscillation around a mean shape when a BEC at equilibrium in a harmonic trap is suddenly released into a disorder potential.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)