According to Ayatullah Sistani:
Question: If a person breaks his oath, what is he supposed to do?
Answer: If a person takes an oath that he will perform an act (e.g. that he will fast) or will refrain from doing an act (e.g. that he will not smoke), but does not intentionally act according to his oath, he should give Kaffarah for it, which means he should set a slave free, or should fully feed ten indigent persons, or should provide them with clothes. And if he is not able to perform these acts, he should fast for three consecutive days.