For harps made from carbon steel I suggest drying with a cloth, and keeping a thin coat of chapstick on the reed/frame when finished playing, to avoid corrosion.
If you do end up with some rust, you can hit it lightly with very fine 0000 grade steel wool.
Handle with care, avoid dropping, or otherwise putting undue pressure on the frame to preserve its form and reed/frame embouchure alignment, which is essential to its quality of sound.
Avoid extreme heat (like direct sunlight inside a car on a hot day) to avoid thermal expansion deformation.