How does python find a module file if the import statement only contains the filename?

http://docs.python.org/3/tutorial/modules.html#the-module-search-path

6.1.2. The Module Search Path

When a module named spam is imported, the interpreter first searches for a built-in module with that name. If not found, it then searches for a file named spam.py in a list of directories given by the variable sys.path. sys.path is initialized from these locations:

• The directory containing the input script (or the current directory when no file is specified).
• PYTHONPATH (a list of directory names, with the same syntax as the shell variable PATH).
• The installation-dependent default.

Note: On file systems which support symlinks, the directory containing the input script is calculated after the symlink is followed. In other words the directory containing the symlink is not added to the module search path.

After initialization, Python programs can modify sys.path. The directory containing the script being run is placed at the beginning of the search path, ahead of the standard library path. This means that scripts in that directory will be loaded instead of modules of the same name in the library directory. This is an error unless the replacement is intended. See section Standard Modules for more information.

For information on the "installation-specific default", see documentation on the site module.

Also, you can see what the current path is by using the sys module

import sysprint(sys.path)

It uses the PYTHONPATH, set as an environment variable, to find packages (folders containing __init__.py files) and modules (or, if already loaded once, retrieves the module object from sys.modules).