Procedures to prepare clean Bi₂Se₃(0001) surfaces from bulk samples and epitaxial FeSe nanocrystals on Bi₂Se₃(0001) are reported. Bi₂Se₃(0001) substrates are prepared by in vacuo cleavage of bulk samples, followed by ion bombardment and annealing cycles. FeSe is prepared by Fe deposition onto Bi₂Se₃ at 303 K, followed by annealing at T ≈ 623 K. We use low-energy electron diffraction, surface X-ray diffraction, photoemission spectroscopy, scanning tunneling microscopy and spectroscopy, and stress measurements to elucidate the correlation between structural and electronic properties of the pristine Bi₂Se₃(0001) and FeSe covered surfaces. Our analysis reveals the formation of epitaxial FeSe nanocrystals with a thickness of three unit cells (1.5 nm). Electron diffraction experiments indicate an anisotropic epitaxial strain in FeSe. A negligible strain close to 0.0 % and a tensile strain of +2.1 % are observed along the in-plane [0110] and [2110] Bi₂Se₃ directions, respectively. The out-of-plane strain is +4.2 %. The role of this strain state for the reported high-T_C superconductivity in bulk FeSe is discussed.