Procedures for the preparation of Bi₂Se₃(0001) surfaces, FeSe atomic layers, and Bi bilayers on Bi2Se3(0001) are presented. Bi₂Se₃(0001) surfaces are characterized by terraces separated by quintuple layer high steps of 0.95 nm height. Epitaxial FeSe islands with lateral extensions of several hundred nanometers and a few unit cell (nm) thickness are produced by Fe deposition at room temperature and subsequent annealing at 650 K. These islands are under an anisotropic in-plane strain (a = 0.377 ± 0.002nm, b = 0.385 ± 0.004nm) with respect to the bulk FeSe reference state (a_FeSe,bulk = nm). Bi bilayers are formed on Bi₂Se₃(0001) by atomic hydrogen plasma etching, which removes Se from the Bi₂Se₃ sample surface. Scanning tunneling microscopy and scanning tunneling spectroscopy are used to characterize the Bi2Se3 substrate and the nanostructures formed on its surface. A differential conductance peak near V identifies a defect-free Bi bilayer on Bi₂Se₃(0001).