On Linux with development tools installed this is straight forward. On Windows, you need to install Cygwin.

So you have a .so file and you need a clue about the API used? To list the symbols you can use one of the following:

1) nm -gC yourLib.so
2) readelf -Ws yourLib.so
3) objdump -TC yourLib.so

Here is a .so lib file, part of the Android HTC Desire phone, and the extracted symbols as .txt files:
so-symbols