To address the significant capital expenditures (CAPEX) and operating expenses (OPEX) associated with each antenna having its dedicated radio frequency (RF) chain in multiple-input multiple-output configuration, various techniques have been introduced, such as analog architectures, hybrid architectures, and index modulation (IM). Moreover, novel antenna architectures, such as graphene-based and dynamic metasurface antennas (DMAs), which leverage the unique properties of graphene and metamaterials, respectively, have been proposed to further reduce CAPEX and OPEX. In this study, we propose novel DMA-based IM schemes that aim to significantly reduce the power-hungry yet expensive RF chains, thereby improving the OPEX and CAPEX. Specifically, we propose a spatial modulation (SM) technique for the DMA architecture, which is achieved by activating either a single microstrip (microstrip-wise SM) with the help of a switching mechanism or a single DMA element (element-wise SM) by manipulating both the DMA reconfigurable weight and a switching mechanism. Our analysis shows that microstrip-wise SM achieves higher signal-to-noise ratios (SNRs) and, consequently, higher spectral efficiency compared with element-wise SM. However, in the high-SNR regime, the element-wise SM performs very close to the microstripwise SM while requiring lower complexity. Furthermore, we propose a generalized spatial modulation (GSM) technique for the DMA architecture, achieved by simultaneously activating multiple microstrips, to further enhance the spectral efficiency. We propose the design of DMA weights to maximize the SNR for the two considered SM schemes, obtaining closed-form solutions. For the GSM scheme, we develop an alternating algorithm to optimize the DMA weight and baseband precoder to maximize the spectral efficiency. Finally, we provide simulation results to validate our analysis and demonstrate the effectiveness of the proposed schemes.