Additional steps for users of CadSoft-Eagle:

Download the file brd_to_dsn.ulp and put it into the subdirectory ulp of your Eagle installation directory.
Start Eagle and open in the control panel of Eagle for example the design my_design.brd.
Choose in the Files pulldown-menu of Eagle the item "execute ULP" and select brd_to_dsn.ulp. A file with name my_design.dsn is generated.
Start the router, push the "Open Your Own Design" button and select my_design.dsn in the file chooser.
After making some changes to the design with the router select "export Eagle session script" in the Files pulldown-menu. A file with name my_design.scr is generated.
Choose in the Files pulldown-menu of Eagle the item "execute Script" and select my_design.scr.