The words alumni, alumnus and alumna are all forms of one noun that was borrowed into English from Latin. In Latin, most nouns have different endings depending on whether the noun was singular or plural or whether it referred to a man or a woman. We do this to a limited extent in English also, usually by adding an s to the end of the noun to show that it's plural (book-books, etc.), but English has many fewer endings than Latin. Most words that have been adopted into English from other languages don't keep all their original endings, but there are some that do, and this is especially true of words from Latin, a carry-over from past times when it was much more likely that educated English speakers had also studied Latin.
In the case of this Latin word, alumnus was the masculine singular, alumna was the feminine singular, alumni the masculine (or the masculine and feminine collective) plural and alumnae the feminine plural. This usage should be followed in Modern English: that is, use alumna to refer to a woman who has graduated from a college or school and alumnus for a man, and use alumni to talk about men or men and women together who are graduates of a school but alumnae when you are talking exclusively about female graduates.
A note about pronunciation: in classical Latin the last syllable of alumni was probably pronounced similarly to the English word knee, but many speakers of English pronounce the -ni of alumni like the -ny in deny. And the -nae of alumnae probably sounded in Latin like the -ny of deny, yet many English speakers pronounce alumnae to rhyme with day. My advice is that if you keep to the original Latin rules for when to use alumnus, alumna, alumni and alumnae, you should also pronounce the endings as they were in classical Latin.