Originally Posted by: HoboBassistThe book I'm using has a crapload of arpeggios at the beginning with absolutely no explanation on muting the open strings.

What is the book?

In classical style there are two basic types of strokes (ways of striking the strings): rest stroke and free stroke. I explain them here:

http://www.guitartricks.com/tutorial.php?input=324

In general, Hunter gave you great advice, just let them ring. In many classical exercises and etudes (Villa-Lobos for example) the notes of arpeggios are understood to ring until you must play another note on the string or you must move your finger or hand from the string. If a rest stroke is required it should be indicated.

Best of success with it!