What glue should I use, to glue drawer liner paper onto a wooden box

Any craft glue........

A spray adhesive.

Aleen's glue products are still my favorites.

Spray and glue. Available at you local big box store.

Try contact paper, it comes out smooth, and you use a rag to move any bubbles out, and it looks great. Paper glue, go to a craft store for that, and see what they have for your type of paper. Contact paper you can wash with a little soap and rag. Good Luck!

Spray adhesive.

Mod Podge.

Spray adhesive will be the easiest.

You could get a small jar of the wallpaper paste used in dollhouses.

If you want to remove the paper with out damaging /marring in the future, just use a thin coat of wallpaper border/vinyl to vinyl glue.