Depends on which part of the 18th century about which you are
talking. Pre-Revolutionary War or post?
Pre-Revolutionary War - Colonial governments issued paper
currency; foreign coins were also used.
Revolutionary War - Colonies continued to issue paper currency
to cover military expenses. The Continental Congress also issued
Continental currency. Both were practically worthless by the end of
the war.
Post-Revolutionary War - The Constitution barred states from
issuing their own currency and the federal government took on
currency issuance. The government began to issue currency after
ratification of the Constitution.