Understanding quantum phases and phase transitions in the presence of symmetries is a central objective of quantum many-body physics. A powerful modern paradigm for investigating this problem is topological holography, which relates symmetries in k dimensions to “bulk” topological orders in (k + 1) dimensions. While conceptually profound, most existing bulk construction methods rely on sophisticated mathematical formalisms and can be difficult to apply to certain symmetry types. In this work, we propose a physically intuitive and versatile method, termed the layered gauging construction, to systematically generate (k + 1)-dimensional (liquid or fracton) topological orders from k-dimensional generalized symmetries. Roughly speaking, the prescription is to stack many layers of k-dimensional quantum systems with certain symmetries into a (k + 1)-dimensional pile, and then sequentially gauge a diagonal symmetry acting on each nearest-neighbor pair of layers. The detailed procedure depends on the specific symmetry types. We have successfully implemented the method in a number of examples in different spatial dimensions, with symmetries that are conventional, higher-form, subsystem, anomalous, nonabelian, or noninvertible. We hence conjecture the method to be very general. For example, from the subsystem symmetry of the 2d plaquette Ising model, we derive the X-cube model and also an anisotropic fracton topological order. Additionally, starting from an anomalous Z2 symmetry in 1d, we construct a new square lattice model realizing the double semion topological order. From a quantum-error-correction perspective, our layered gauging construction may be viewed as a generalization of the hypergraph-product construction beyond the standard Calderbank-Shor-Steane setting.