Dialog programs in ABAP consist of multiple linked objects including screens, module pools, and subroutines. Screens are composed of fields, layouts, and flow logic to transfer data between the dialog processor and ABAP processor. Module pools contain modularized ABAP code organized into include programs for global data, PBO modules, and PAI modules. These components are created using tools like the screen painter and editor and linked together through the main program to form an executable transaction when a transaction code is assigned.