The following is taken from Stilman and Harkins "Introductory Russian Grammar, an excellent textbook: "The conjunction и connects several members of a sentence to which the statement made is equally applicable. Иван и Ольга дома. Ivan and Olga are at home. The separative conjunction а (always with a comma before it), is used when two different statements are made about two members of a sentence. Иван тут, а Ольга там. Ivan is here, and (but) Olga is at home. The separative а must be used with statements that are merely different, even when, as in the example above, they are not felt to be conflicting or contrasted. The conjunction а is also used in sentences of the type 'This is A, but not B', or 'This is B, and not A'. Она не тут, а дома. (or: Она дома, а не тут.) She is not here, but at home. (or:She is at home, and not here.) Он не студент, а журналист. (or: Он журналист, а не студент.) He is not a student, but a journalist. (or: He is a journalist, and not a student)"

"а" when it means while, yet, but "и" when it means and

I'll give you a few examples. Испекла фруктовый торт для него, а он не пришел. I made a fruit cake for, but he did not show up. В России зима, а в Автралии лето. It's winter in Russia while it's summer in Australia. Испекла фруктовый торт для него, и он пришел. I made a fruit cake for him and he did show up.