Simulated observations of a $10dg times 10dg$ field by the Microwave Anisotropy Probe (MAP) are analysed in order to separate cosmic microwave background (CMB) emission from foreground contaminants and instrumental noise and thereby determine how accurately the CMB emission can be recovered. The simulations include emission from the CMB, the kinetic and thermal Sunyaev-Zeldovich (SZ) effects from galaxy clusters, as well as Galactic dust, free-free and synchrotron. We find that, even in the presence of these contaminating foregrounds, the CMB map is reconstructed with an rms accuracy of about 20 $mu$K per 12.6 arcmin pixel, which represents a substantial improvement as compared to the individual temperature sensitivities of the raw data channels. We also find, for the single $10dg times 10dg$ field, that the CMB power spectrum is accurately recovered for $ell la 600$.