The question is extremely vague. “Ancient” covers a large period of time that had varied technologies. “Communication” is also a very vague term. That being said, I will attempt to give an answer.
I am assuming that you are asking about human communication. One of the things that distinguishes humans from animals is speech. Probably the most ancient means of communication was speech. Hand gestures, body language, and facial expressions are also a means of communication. Dance and music were also very ancient means of communication.
Messengers with verbal messages, signal fires, totems, banners, cave art, etc. were ancient means of communication that predate history.
Proto alphabets and pictographs were used as early as 60,000 years ago. Such script was found on egg shells dating back that far and found in southwestern Africa.
Genuine writing began as early as 5,000 years BC with the Vinca script (although this is disputed). It is undisputed that cuneiform script was in use in what is now Iraq about 3,000 BC. This early writing was typically impressed on clay tablets and allowed to dry. Small tablets could be transported between distant locations. Some script was also present on pottery. Rudimentary codes were used for distant communication with signal fires. Drums could be heard at great distances and were also used to communicate. Once paper was invented, things really took off, literally. Messenger pigeons were used as early as 1150 in Baghdad and also later by Genghis Khan. This ancient means of aerial communication was still in wide use in World War I.
More common were couriers on horseback that would take written messages quickly between people at distances. In ancient Persia (Iran) they had messengers, called angros that would carry messages in stations that had a day's ride distance along the royal road. The riders were exclusively in the service of government. A message could be transported from Susa (south western Iran) to Sardis (western Turkey), a distance of 1,677 miles in just seven days. The same journey took ninety days on foot. This type of system was later used by the Romans. Messages were also transported by boats and ships.
Even ancient communication could be relatively fast.
