You can't usually tell just by looking at the library. You need the header file as well. Then you can find out what functions are in the library by looking at the header file and reading the documentation.
How do you use the functions: as explained above. Let's say libffmpeg.so contains a compiled function void LoadFile(char *fileName). In the header file (let's call it libffmpeg..h) there will be a line:
void LoadFile(char *fileName);
Then your code needs (a) to include that header file:
(b) call the function:
void myFunc(char *fnam)
and (c) to link with the library to avoid "undefined symbol" errors:
gcc test.c libffmpeg.so -o test