We present a numerical framework bringing together a structural and a surface-energy minimization model to compute nano- and microorigami self-folding processes, that are three-dimensional in nature. A liquid drop, initially at rest on the template, triggers the spontaneous folding and deforms dynamically with the template. As application, the self-folding of thin two-dimensional templates into pyramidal microstructures is simulated. Each template is composed of a fixed regular base connected to rigid triangular side panels by two elastic hinges. We presently determine the condition, at which the transition from partial to full drop encapsulation occurs. The present model makes use of phase fields to numerically represent the drop and the template. This allows to: (i) develop an efficient computational method, which incorporates time-derivative terms and (ii) study three-dimensional complex self-folding processes.