We employ spectroscopic and photometric data from SDSS DR7, in a 500 sq degree region, to understand the evolution of dwarf (~M*+2<M_z<M*+4) galaxies in the Coma supercluster (z=0.023). We show that in the Coma supercluster, the red dwarfs are mostly concentrated in the dense cores of the Coma and Abell 1367 clusters, and in the galaxy groups embedded in the filament connecting them. The post-starburst (k+A) dwarfs however are found in the infall regions of the Coma and Abell 1367 clusters, and occasionally in galaxy groups embedded along the filament, suggesting that strong velocity fields prevalent in the vicinity of deep potential wells may be closely related to the mechanism(s) leading to the post-starburst phase in dwarf galaxies. Moreover, the blue colour of some k+A dwarfs in the Coma cluster, found within its virial radius, suggests that the star formation in these galaxies was quenched very rapidly in the last 500 Myr. More than 60% of all red dwarf galaxies in the supercluster have 0-3 ang of H_\delta in absorption, which suggests that a major episode of star formation occurred in a non-negligible fraction of these galaxies, ending within the last Gyr, allowing them to move to the red sequence. The distribution of the blue dwarf galaxies in the Coma supercluster is bimodal in the EW(H_\alpha)-EW(H_\delta) plane, with one population having very high emission in H_\alpha, and some emission in H_\delta. A sub-population of blue dwarfs is coincident with the red dwarfs in the EW(H_\alpha)-EW(H_\delta) plane, showing absorption in H_\delta and relatively lower emission in H_\alpha. We suggest that a large fraction of the latter population are the progenitors of the passive dwarf galaxies that are abundantly found in the cores of low-redshift rich clusters such as Coma.