how would you hang a painting made out of wood?

it has four sides that are painted, it is it is probably at least an inch deep and hollow on the back inside.
i don't want to just lean on a shelf & i don't want to have to drill any holes in it to add hooks.
is it as simple as drilling some screws in the drywall and leaving them stick out enough,?

maybe i am over analyzing it.

It's the wall you're thinking about? the picture is strung? If so, how about those hooks with the three tiny pins on the back. You just give it a couple of knocks with a hammer.The pins go in at an angle so they do stick well to the wall.

these...

Sounds like it has no hooks or wire on the back for hanging, but it does have a 'hollow' on the back, is that right?

If so you're probably right - just use long screws with either lead or plastic anchors (or those expand-o-sleeves that buckle on the back side of the wall -- these are strongest if it's heavy), let an inch or less of the screws remain exposed, and have them support the inside 'lip' of the back-hollow. It'd be better to use 2 screws, one near each top corner, than try to balance it on one - just make sure the 2 screws are level ...

oooo yeah, i'd buy a laser level for this project...