D.C. (da capo – literally, from the top): Tells you to repeat from the beginning.
D.C.al fine: tells you to repeat from the beginning until you get to the word fine, where you stop.
D.C. al coda: Tells you to repeat from the beginning until you get to the word coda and then jump to the coda sign.
The Coda sign shows a jump forward in the music. Only used after playing through D.C. al coda or D.S. al coda.
D.S. (Dal segno literally – from the sign): Tells you to repeat playing from the segno.
D.S. al fine: Tells you to repeat from the segno until you get to the word fine, where you stop.
D.S.al coda: Tells you to repeat playing from the segno until you get to the word coda nd then jump to the coda sign.
This seems complicated, however, when you can listen to the music and follow it on the page it will become clear.