There are a number of explanations as to how the $ sign developed.
The most common is that the sign comes from the sign originally used for the peso, also known as the Spanish dollar. The sign used in Spain and Mexico for peso – a P followed by an S – gradually came to be written with the S overlaying the P, thereby giving rise to the $ sign. Support for this explanation comes from business correspondence in Britis North America from the 1770’s between British, Americans, Canadians and Mexicans using the $ sign. The term dollar and the dollar sign were adopted as US currency in 1785.
An alternative explanation is that the sign comes from the figure 8 with a stroke through it, denoting pieces of eight, another name for the Spanish dollar. (The Spanish dollar, a silver coin, was also known as the real de a ocho, or eight-real coin, a dollar being worth 8 reales, hence the term pieces of eight, Robert Louis Stevenson’s tale Treasure Island and its depiction of Long John Silver’s parrot constant calling out “Pieces of Eight” led to the association of pieces of eight with pirates).
The name 'dollar', however, derives from the Dutch or Low German word daler (in German taler or thaler) - originally Joachimstaler, referring to a coin from the silver mines of Joachimstal, in Bohemia (now Jáchymov in the Czech Republic), which opened in 1516.
The pound sign - £ - being the symbol for the basic currency unit of the United Kingdom, derives from a capital "L", standing for libra, the basic Roman unit of weight, which is in turn derived from the Latin word for scales or a balance. The pound became a British unit of weight, and the pound currency unit was so named because it was originally the value of 1 pound Tower Weight (326 g)] of fine (pure) silver.