This is the first of two papers that develop theories and numerical methods for photoionization microscopy of hydrogen atoms in strong electric fields, in semiclassical and quantum-mechanical frameworks, respectively. In this paper, semiclassical open-orbit theory is presented to describe the propagation of outgoing electron waves to macroscopic distances. Spatial distributions of electron probability densities and current densities are predicted. The open-orbit theory, based on an assumption that electron waves propagate along classical paths from a pointlike source to a detector, provides a clear and intuitive physical picture to interpret structures of observed geometrical interference patterns in photoionization microscopy. We calculate photoelectron ejection of hydrogen atoms in electric fields, and comparison is made with quantum-mechanical results, which will be detailed in the second paper [Zhao and Delos, Phys. Rev. A 81, 053418 (2010)]. A strong quantum tunneling effect has been found. Such a tunneling effect should be visible in the experiment.