Is it possible to make an audio player with an sd card and an Arduino nano? If so could you give some guidance
Yes, look at these MP3 player modules.
Send a simple serial command at 4800 bps to start a song playing, also supports stop, pause, etc commands.
Is an MP3 module needed
dustyloshe: Is an MP3 module needed
Absolutely, unless you are happy with a buzzer kind of sort of playing music one note at a time.