The 3D printing of soft materials is challenging mainly due to their rheological behavior. The 3D extrusion-based printing was correlated with the rheological properties for each stage of the process. A protocol to obtain an optimal ink was defined and Laponite/alginate mixtures were analyzed. All mixtures exhibited a pronounced shear-thinning behavior. Higher alginate concentrations partially hindered the rheology modifier effect of Laponite. The filament formation during extrusion and good printability were observed for Laponite concentrations of at least 5 wt%. The optimal ink was defined as a function of the viscosity profile, the filament formation ability, the flow-point and the solid-like/liquid-like behaviors. The viscosity recovery test demonstrated an instant structure recovery for the optimal ink, which did not present shear rate dependence. Jointly, an extrusion-based modular printer head was developed and tested to be compatible with open source 3D printers. Finally, the 3D printed gels were crosslinked to obtain single (SN) and double network (DN) hydrogels. In these latter, a second network precursor of poly(acrylamide) was used. As established, the rheological characterizations constitute a powerful tool to analyze the printability of soft materials.