Confer and consult are very closely related in meaning, and each has senses that are synonymous with the other’s. But as is so often the case with near-synonyms, there are contexts in which one word is preferable to the other.
If you confer with someone, it is entirely possible that you will be seeking advice, but you could also simply be having a discussion (“they conferred privately before making a decision”). If you are consulting someone or something, it is more likely that you are seeking advice (“he consulted his doctor before deciding on a course of treatment”). Consult is unambiguously the correct choice when one is seeking guidance or information from a non-human source; you would consult (not confer with) a dictionary for information on a word.
The sense of confer that is concerned with giving something (as in, “education confers many benefits”) is not shared by consult.