Equipment-free pumping is a challenging problem and an active area of research in microfluidics, with applications for both laboratory and limited-resource settings. This paper describes the pumping lid method, a strategy to achieve equipment-free pumping by controlled generation of pressure. Pressure was generated using portable, lightweight, and disposable parts that can be integrated with existing microfluidic devices to simplify workflow and eliminate the need for pumping equipment. The development of this method was enabled by multi-material 3D printing, which allows fast prototyping, including composite parts that combine materials with different mechanical properties (e.g. both rigid and elastic materials in the same part). The first type of pumping lid we describe was used to produce predictable positive or negative pressures via controlled compression or expansion of gases. A model was developed to describe the pressures and flow rates generated with this approach and it was validated experimentally. Pressures were pre-programmed by the geometry of the parts and could be tuned further even while the experiment was in progress. Using multiple lids or a composite lid with different inlets enabled several solutions to be pumped independently in a single device. The second type of pumping lid, which relied on vapor-liquid equilibrium to generate pressure, was designed, modeled, and experimentally characterized. The pumping lid method was validated by controlling flow in different types of microfluidic applications, including the production of droplets, control of laminar flow profiles, and loading of SlipChip devices. We believe that applying the pumping lid methodology to existing microfluidic devices will enhance their use as portable diagnostic tools in limited resource settings as well as accelerate adoption of microfluidics in laboratories.