1. Import biblatex with your favourite options
\usepackage[<options>]{biblatex}
2. Specify the names of your bibliography database(s).
\addbibresource{<your .bib file names>}
3. Add a refsection environment for each chapter and print the bibliography at the end of the chapter.
\chapter{From K\"onigsberg to G\"ottingen}
\begin{refsection}
… % Lots of text and citations omitted.
\printbibliography[heading=subbibliography]
\end{refsection}
4. Run latex on your LaTEX source file. This will create an auxiliary file for each refsection with a \printbibligraphy command in it. The names of theses auxiliary files are of the form <base name><number>- blx.aux, where <base name> is the base name of your main document.
5. Run bibtex on each auxiliary file.
6. Run LaTEX twice.