How do I compile and deliver my application without requiring installation of shared libraries on other machines

Maybe I can simply share the file along with the executable, like I would do in Windows with DLL files?

It 'depends' on the 'dependencies'.

Use the command ldd to figure out, which libraries are required by a library or program. Those required libraries have to be present (installed) on the target system.

Even if a required library is installed on the target system, it could be possible, that the required version is not available.

That's why the different (linux) systems have their package management systems, which are able to resolve the dependencies and install them automatically.