There are two different types of programs which you will use (although confusingly sometimes one program can do both).
The first is CAD which stands for Computer Aided Design. You use a CAD program to create the design you want to cut. CAD programs can be 2d (like Inkscape or Adobe Illustrator), or 3d (like Sketchup, SolidWorks, Fusion360).
The second type of program you will need is a CAM program which stands for Computer Aided Machining (or Manufacturing depending on who you ask). This step takes your design and converts it into cuts for the machine to make. The file you will generate at the end is called a gcode file.
Check out this video. It’s a little out of date at this point, but it should give you an idea of what the process looks like: