Time zones weren't "discovered" -- they are arbitrary constructs to fit local time into a 24-hour day -- but if what you're asking is when people knew that time was different in different parts of the world, that was known in classical antiquity. I wrote about this more here. However, before railroad travel, worry about time zones was fairly meaningless, because you couldn't travel across them fast enough to really notice anything we'd call "jet lag" today. Time zones were first used by rail operators to solve the problem of scheduling trains -- bad things happen when they run into each other.

The problem with establishing time zones, of course, is where to start and end them -- at what point on the globe is 0 hour set, and (conversely) at what point on the globe is +12 set, that is, where does the day/date change? Because knowledge of time being different in different places is useful for navigation (if I have a very accurate clock set to local time at a known location, and if my clock is saying it's 1 p.m. when it's at local noon, I'm 1 hour west of a specified place at that location, and I can work out my position with that knowledge and a bit of math). This is the position that navigators in Europe found themselves in during the late 1700s and early 1800s -- the first clocks accurate enough to show that weren't built before 1760 or so, and not thought good enough to use at sea until 1775 or so, and too expensive to be bought in large numbers through the 1840s. I wrote more about this here.

Anyways, that known location, or 0 hour, could be pretty much any line of longitude on the globe. Many mariners would set their chronometers based on the noon reading at the Royal Observatory, at Greenwich in England, and convention tended to favor using that. An International Meridian Conference in 1884 formalized this, and also established the idea of universal time.

To illustrate how time zones are arbitrary, you can consult a time zone map and notice how time zones often are determined by country boundaries -- in particular the International Date Line zigs and zags to accommodate island nations, and the boundary between Central and Eastern time in southern Indiana continues to vex local residents.