A good masquerade mask isn't something you wear once and throw away, but it does need a little care to hold up for a second event, a photo re-shoot, or just to look good sitting on a shelf between now and next Halloween. How you clean and store it depends mostly on what it's made of.
Lace masks
Lace masks are the most sensitive to moisture and heat. If makeup transfers onto the lace, spot-clean gently with a barely damp cloth rather than soaking it, and let it air-dry completely flat before putting it away. Avoid ironing lace directly — if it needs to be reshaped, steam it from a few inches away instead.
Laser-cut metal masks
Metal filigree masks hold up the best of the three materials, but the painted or plated finish can scratch, and any rhinestone accents are usually glued rather than set, so they can come loose if the mask is dropped or rubs against something in storage. Wipe with a dry or barely damp soft cloth, and if a stone does come loose, a small dot of clear-drying craft glue will usually reset it.
Feather masks
Feather masks are the most delicate to store. Feathers crush and mat if anything is stacked on top of them, and humidity can cause them to droop or clump. Store feather masks upright or hanging rather than flat under other items, and if the feathers do get compressed, a light steaming from a distance (never direct contact) will usually help them spring back.
General storage tips
For any mask, the two things that matter most are avoiding direct sunlight, which fades color over time, and avoiding humidity, which affects lace and feathers especially. If your mask came with any packaging, that's usually the best storage option since it's sized to hold the shape without crushing it. Otherwise, a shallow box or drawer where the mask isn't pressed against anything else works well.