Wash a wooden spoon by hand with mild dish soap and warm water, rinse all sides, towel-dry it, then let it stand until completely dry. Do not soak it or use a dishwasher unless the maker explicitly says those methods are safe for that utensil.

Clean food residue without soaking
Wash the spoon soon after cooking so food does not dry onto the wood. Use mild dish soap and warm water, rinse both sides and the handle, then dry it with a towel. OXO’s directions for its beechwood utensils add that the spoon should stand until fully dry; they also say not to submerge OXO wood products or put them in a dishwasher. For stuck residue, follow the utensil maker’s cleaning directions instead of leaving the whole spoon in water.
For an odor or a dry surface
OXO’s wood-care guide gives odor-removal methods for its wood products, including an equal-parts vinegar-and-water wipe and lemon with coarse salt, followed by washing, drying and conditioning. It also suggests a water-drop check: if droplets absorb immediately, OXO recommends oiling and waxing; if they bead, it says the wood is conditioned. Its guide recommends products made for wood utensils or cutting boards and warns against cooking oils that can turn rancid. These treatments are specific to OXO’s guidance; check another spoon maker’s finish and instructions before using them.
Sources: OXO wood-care instructions and its wooden spoon listing.