How do I package the shared libraries
(.so files) with an executable let's say for linux and make sure that the program links to those shared libraries.do I just put the .so files and the executable files in the same directory or do I have to do something else.

I haven't coded in c++ in about a decade, but if I remember correctly, what you have to do is open a terminal and type: man ar

You could for example use cpack (https://cmake.org/Wiki/...) from CMake which allows you to create deb or rpm packages or other for the target distribution. You will will need to configure where your library should be deployed (/usr/lib - /usr/local/lib or whatever path).
If you want to make sure your library will be linked before any library on the clients machine you can add an rpath (https://en.wikipedia.org/wiki/Rpath) to your deployed library.