PostgreSQL supports left unary, right unary, and binary operators. Operators can be overloaded; that is, the same operator name can be used for different operators that have different numbers and types of operands. If there is an ambiguous situation and the system cannot determine the correct operator to use, it will return an error. You may have to type-cast the left and/or right operands to help it understand which operator you meant to use.
Every operator is "syntactic sugar" for a call to an underlying function that does the real work; so you must first create the underlying function before you can create the operator. However, an operator is not merely syntactic sugar, because it carries additional information that helps the query planner optimize queries that use the operator. Much of this chapter will be devoted to explaining that additional information.
Read the upstream documentation. For corrections, first check the current version.