Psh.... "In my day...."
Get a list of the standard pieces of music you "should know."
Then you need to know the composer's full name, correct spelling, birth and death dates. Date of composition. Full name of the composition, in the original language (I think, but that means Cyrillic for text, German, French, Spanish, whatever. And then you'll want to be able to pronounce it correct so you don't look stupid, but that you'll want the in between pronunciation that's not purely that language because it's odd but not your language's accent because it still looks uneducated, so stick with something in between...) But date of composition, title, and then movement.
Be able to name the composer/dates, composition/dates/title/movement. Being able to name the style/period is cake, so you'll need to be able to explain why elements you hear are representative of that style. Still not too difficult since it's some general composer traits you can memorize and generally pick out from pieces. The most important part is rote memorization of the pieces and info.
Here's a list of 30 pieces for next week. You'll get another 30 pieces to be able to identify for the following week, except we can ask you any of the previous pieces still. And if the professor gets bored they'll find a recording that's an arrangement (ex. piano arrangement of an orchestral piece) to really mess with your mind.
Theory or ear training 101. I remember that.... You end up doing a lot of listening and absorb the style. I figured out to memorize the info by rote, just flat out memorization with some mnemonics. Chopping up the pieces into small audio clips helps hugely so you only have to listen through the whole piece once. And then lots of practice on identifying those sound clips from a mixed up order. Using a computer would probably between using cassette tapes like I did.
You can also get good at instantly recognizing a composer's style. You might not know the piece but you'll know the composer.