Programmable metasurfaces provide an innovative scenario to carry out promising control of electromagnetic waves. However, most works focus on the manipulation of only linearly polarized (LP) or circularly polarized (CP) waves, and multilayer configurations are typically desired due to the existence of direct current biasing networks. Here, a general strategy for designing programmable metasurfaces for the manipulation of both LP and CP waves is proposed and verified. As a result, the real-time programmable manipulation of quad-LP (x-polarized, y-polarized, upolarized, v-polarized) and dual-CP (right-hand, left-hand) waves could be achieved. Moreover, by placing both the direct current biasing network and the finely designed isolation circuit on top of the metasurface, only a single dielectric layer is required for such a programmable metasurface. As an example, a single-layer programmable metasurface consisting of 16 × 16 meta-atoms is designed, fabricated, and measured. The PIN diodes incorporated into each meta-atom are used as active components to provide a 1-bit reflective phase control. By shifting the working states of each PIN diode in the meta-atom, wide-angle beam scanning can be obtained. Both the simulated and measured results verify the capacity of the proposed strategy and demonstrate that the designed single-layer programmable metasurface exhibits stable beam scanning for both LP and CP waves, enabling promising applications in future wireless communications.