To perform a song, you must buy an instrument and music sheet. These can both be bought from merchants across Antaloor, more specifically from bards in Bayan or Hatmandor.
Some songs are more complicated than others, but I personally recommend "Tuesday Market" on the drum. It has a fairly easy beat and is of decent length. Two Worlds II can lag pretty badly in cities sometimes, which can cause the notes to lag. To reduce lag and frustration, I recommend playing this song out in the wilderness where there aren't many people, as this will reduce lag significantly.