This paper presents a systematic method for renormalizing the AdS/CFT prescription for computing correlation functions. The method involves regularizing the bulk on-shell supergravity action in a covariant way, computing all divergences, adding counterterms to cancel them, and then removing the regulator. The approach is applied to pure gravity up to six dimensions and gravity coupled to scalars. The method provides a holographic reconstruction of the bulk spacetime metric and fields from conformal field theory (CFT) data. Knowing which sources are turned on allows the asymptotic expansion of the bulk metric and fields near the boundary to high order, capturing all infrared divergences of the on-shell action. To continue the reconstruction, new CFT data, such as the expectation value of the dual operator, is needed. The paper provides explicit formulae for the holographic stress-energy tensors up to six dimensions, showing that both gravitational and matter conformal anomalies are correctly reproduced. The conformal transformation properties of the boundary stress-energy tensors are also discussed. The results are presented for spacetime dimensions up to six, with the stress-energy tensor expressed in terms of the boundary metric and its curvature. The paper also discusses the conformal transformation properties of the stress-energy tensor, showing how it transforms under conformal transformations in both even and odd dimensions. The results are consistent with known conformal anomalies and the behavior of the stress-energy tensor in conformally flat backgrounds. The paper concludes with a discussion of how matter fields are encoded in the CFT, showing that the same pattern of determining divergences and finite parts applies to matter fields as to gravity.This paper presents a systematic method for renormalizing the AdS/CFT prescription for computing correlation functions. The method involves regularizing the bulk on-shell supergravity action in a covariant way, computing all divergences, adding counterterms to cancel them, and then removing the regulator. The approach is applied to pure gravity up to six dimensions and gravity coupled to scalars. The method provides a holographic reconstruction of the bulk spacetime metric and fields from conformal field theory (CFT) data. Knowing which sources are turned on allows the asymptotic expansion of the bulk metric and fields near the boundary to high order, capturing all infrared divergences of the on-shell action. To continue the reconstruction, new CFT data, such as the expectation value of the dual operator, is needed. The paper provides explicit formulae for the holographic stress-energy tensors up to six dimensions, showing that both gravitational and matter conformal anomalies are correctly reproduced. The conformal transformation properties of the boundary stress-energy tensors are also discussed. The results are presented for spacetime dimensions up to six, with the stress-energy tensor expressed in terms of the boundary metric and its curvature. The paper also discusses the conformal transformation properties of the stress-energy tensor, showing how it transforms under conformal transformations in both even and odd dimensions. The results are consistent with known conformal anomalies and the behavior of the stress-energy tensor in conformally flat backgrounds. The paper concludes with a discussion of how matter fields are encoded in the CFT, showing that the same pattern of determining divergences and finite parts applies to matter fields as to gravity.