I'm creating a billboard with cutouts. How do you represent the cutout portion.
Do you just outline the parts to be cutout with a solid line like a crop mark would do, except the cutout goes around a person's body in the picture.
If by cutout you mean a dieline/diecut, you seem to describe it right.
You simply draw a path/outline around the area where you want the cut out to be, a bit as you would if you had to indicate to someone how to cut a shape on a sheet of paper. That line will be solid (eg. not dashed or dotted).
Like the pink line in the example below:
That line should be created in vector ideally, and you can use a spot color to make sure the printer separate it from the other colors. You'll need to mention to the printer which file is your dieline and provide it separately if you don't want issues (unless he specifies otherwise!)
That means your dieline (the shape representing the cutout) in a file and the layout (your design, the billboard) in another. You can provide provide them in the same file, just make sure the dieline is overprint, in spot color and in vector.
For your printed design, you'll create it as you'd normally do for any other large scale design, with bleed and whatever requirements your printer gave you.
Here's a link with some info on another dieline project. The technique should be similar for your own project. Of course if you can, using vectors is always a good idea!
If you have questions, your printer will be able to give you details about what he really wants.
He'll probably need a specific amount of bleed, will suggest you the right resolution and file format for your print-ready file, maybe he'll want your dieline to be a certain thickness, maybe there's curves or corners or shapes that cannot be achieve (eg. a star), etc. That's not details we can really provide you unfortunately.