The interactions between phonons and electrons induced by the dopants or the substrate of graphene in spectroscopic investigation reveal a rich source of interesting physics. Raman spectra and surface-enhanced Raman spectra of supported and suspended monolayer graphenes were measured and analyzed systemically with different approaches. The weak Raman signals are greatly enhanced by the ability of surface-enhanced Raman spectroscopy which has attracted considerable interests. The technique is regarded as wonderful and useful tool, but the dopants that are produced by depositing metallic nanoparticles may affect the electron scattering processes of graphene. Therefore, the doping and substrate influences on graphene are also important issues to be investigated. In this work, the peak positions of G peak and 2D peak, the I2D/IG ratios, and enhancements of G and 2D bands with suspended and supported graphene flakes were measured and analyzed. The peak shifts of G and 2D bands between the Raman and SERS signals demonstrate the doping effect induced by silver nanoparticles by n-doping. The I2D/IG ratio can provide a more sensitive method to carry out the doping effect on the graphene surface than the peak shifts of G and 2D bands. The enhancements of 2D band of suspended and supported graphenes reached 138, and those of G band reached at least 169. Their good enhancements are helpful to measure the optical properties of graphene. The different substrates that covered the graphene surface with doping effect are more sensitive to the enhancements of G band with respect to 2D band. It provides us a new method to distinguish the substrate and doping effect on graphene. PACS: 78.67.Wj (optical properties of graphene); 74.25.nd (Raman and optical spectroscopy); 63.22.Rc (phonons in graphene).