There is a situation when one should be concerned about dreams. If a person is about to set out on a journey by road or by boat and in his dream he was warned that he should not go on the trip, he should be concerned about this and refrain from going to that place. Likewise, one should not tell other people that he dreamed something that is not good about them. The best thing to do is to not attempt to decipher the interpretations of dreams, for he who increases knowledge increases pain (Koheles 1:18), while He who walks in innocence will walk securely (Mishlei 10:9).
But Praiseworthy is the man who always fears (ibid. 28:14) — even without a dream. One should think about the fact that due to the nature of Man, humans are always susceptible to all the calamities that come upon the world. So, one should do whatever he can of teshuvah (repentance) and good deeds, for they act as shield against calamity.
If one had a dream on Shabbos or on another day when it is forbidden to fast, it is better that he not worry and he should not fast on Shabbos. Instead, he should accept upon himself to fast two other days during the week, and he should recite the prayer for correcting a dream that is said during the Priestly Blessing. His heart should be confident in Hashem, without fear, and Hashem will be a shield for him.