How did people send messages in olden days?
By "olden days" I will assume you mean the days before technology, or perhaps even the days before the telephone was in widespread use. Letters were a common means of communication prior to the electronic age. Unlike today, when letters take as many as two to three days or longer to travel across the continental United States by mail, letters written during the Victorian era could be exchanged on a much faster basis. Generally the wealthy classes had servants delivering letters to local residents by carriage or horseback; and in this way an urgent correspondence could take place and several letters a day could be sent and received. The "Pony Express" was a method used to deliver mail in the western states after the Civil War ended and settlements sprung up slowly with the building of the railroads. Horses were used and could cover an amazing amount of territory in a short period of time, making it a very efficient message delivery system.
The invention of the telegraph in the 1830s did allow a sort of electronic message to be sent, but this was mainly for military usage. However, the telegraph could be used to send an urgent message for personal delivery called a telegram. When a soldier was killed in war, as during World War I or World War II, the family would often be notified by a telegram sent by the US government.