How to open directories in geany IDE?

Create a new Geany project (Project > New) and set the directory to where your project files are.

I think you are mistaking the 'Documents' tab seen in the sidebar for the 'File Browser'. To see the File Browser go to Tools > Plugins and enable tick/check the File Browser plugin.

Edit: The Filename field creates the Geany project file (ProjectName.geany). The Base Path is used to run the Build menu commands (for compiling etc).

It is recommended to keep all of your files in the same directory created in the Filename field.

Check out the plugin "Project organizer". It's available together with a bunch of other plugins for Geany, get it by apt-get install geany-plugins.

With Project Organizer project creation works intuitive, you get a tree-view and code auto-completion reads every file in the project (not just the currently opened ones like it would otherwise).