What is the best way to smooth wood on apple crates

Rasp. or sandpaper & Block

Sandpaper is always the best way, might take a little while but wait till you see the results.

Sanding block

Sand them with a fine grit sand paper.

I would say just good old fashioned sand paper. I would use a medium then a fine with a electric orbital sander and then by hand in the hard to reach places.

Electric hand sander plus sheets of sandpaper to get between the boards and inside corners will do the job. Splinters not welcome! 😇🍁