Spectral Sequences are a useful tool in Algebraic Topology providing information on homology and homotopy groups, but they are not real algorithms except in some particular cases. On the contrary, the effective homology method provides algorithms for the computation of homology groups of complicated spaces, and in particular it allows to determine the homology groups of some spaces related to the most common spectral sequences. In this talk, we explain how the effective homology technique can also be used to obtain, as a by-product, an algorithm computing every component of the corresponding spectral sequence. These methods have been concretely implemented as an extension of the Kenzo computer program.