To export one of your layers to an ESRI Shapefile click Menu - Export a layer - Export to SHP file.
You will be prompted to select a layer and then click the Export button. Several files will be generated which together form a "set" of shapefiles representing the selected layer. Because of the limitations of DBF files, this export tool also generates a CSV file accompanying each Shapefile set which contains a non-truncated version of the same data. If the layer contains any attachments, a hyperlink to each attachment will be included in this exported data. To download the actual documents use the Export Attachments tool.
See other Import and Export options.