As Tom said, keeping them away from humidity will help a great deal in preventing this from happening.
Also, avoid them touching eachother. When dissimilar metals are in contact, corrosion will occur.
Tomato sauce, lemon juice or oxalic acid will clean them, however long exposure to these will strip the patina. Tomato sauce and lemon juice are a bit milder than oxalic acid.
Once clean, wiping the plates with a lightly oiled cloth should help to protect them from moisture.
…Mark