That's going to be a fun job. It should have been prefinished before installing.
Going to have to tape off anything you do not want the stain to touch with 2" wide tape, no mention of where this crown is installed so we will have to guess. Anything below it will need so plastic to cover it to stop the stain from touching it.
I'd use Gel stain not a liquid stain for more control and less dripping. Just brush it on let it sit a few min. and wipe it off with a lint free cloth. (like an old Tee shirt. Make sure to wear rubber gloves to keep it off your hands.