What is a 1924 silver liberty head dime worth?

This dime is more commonly refered to as a "Mercury Dime," although you are correct that the head on the obverse is meant to be a representation of Liberty. The value depends on condition and mint mark. A 1924 dime with no mint mark, signifying that it was made at the Philadelphia mint, is worth about $1.50 in "Good" condition (which is not not actually very good at all), $2.75 in "Fine," $13.50 in "Extremely Fine" and $42 in "Uncirculated MS-60". The same coin with an "S" (signifying San Francisco) or "D" (signifying Denver) mint mark on the bottom of the reverse, just to the right of the Word "ONE", is worth about $3.00 in "Good" condition, about $5.50 in "Fine," about $60.00 in "Extremely Fine" and about $175.00 in "Uncirculated MS-60".