We have investigated the effect of atomic substitutions in the FeSe system, which exhibits the simplest crystal structure among the iron-based superconductors. An enhancement of the superconducting transition temperature Tc was observed with the substitution of S or Te for Se; the Tc increased with S substitution by up to 20 %, and also increased with Te substitution up to 75 %. In contrast, Co or Ni substitutions for the Fe site significantly suppressed superconductivity. In this work we present a detailed description of the substitution technique employed to determine Tc in the FeSe system.