On Windows I just use the "release"- Folder and add all necessary DLL files and start the .exe . Is there an easy way like this for Linux? Can somebody please tell me Step-by-Step how to do this in QT Creator or point me to a tutorial?
Once you have built your program for a Linux target you do exactly the same thing with the program files. On Linux the directory containing the program executable is not normally checked for dynamic libraries so you need to run you program indirectly through a wrapper script. The process is described in the friendly manual: Deploying an Application on X11 Platforms: Creating the Application Package

The equivalent of Dependency Walker on Linux is the command "ldd prog_file_name" but you should not need it if for every file you deployed for Windows you have a corresponding file for Linux.