What was it like before the existence of time zones? When were they established?

In 1883, time zones that resembled fairly closely the modern four time zones in the US were adopted by railroad companies as a way to standardize their schedules. The system was called "Standard Railway Time," or SRT. Because rail had made trips so much shorter, differences in time between destinations was significant. Before time zones, time was found locally, using stars or based on the passage of the sun. This lead to multiple, overlapping schedules for trains, which sometimes caused accidents when it was unpredictable when a track would be occupied. After the shift to the SRT system of time by railroads, cities would often follow, to keep "town time" the same as "train time."

The first source also indicates that in 1884, the "International Meridian Conference" was held to standardize time, which was something also of interest to astronomers and other scientists. Greenwich England was chosen as the "starting" meridian line, fairly arbitrarily, because it was the site of the Royal Observatory. In 1893, international timezones similar to the ones created earlier by US railroads were implemented, with 24 meridians around the globe.

Now, this is, of course, a modern and Western history, encouraged by the increased speed of communications and transportation technology, which made standard time really essential. However, it certainly is possible, and somebody else around here could probably tell you about time zones or similar ideas in earlier history, but this answer is probably roughly what you were looking for.