When were the first timezones established?

Not necessarily the first time zones... but if you're looking for primary sources on the logistics and mechanics of moving to a formal time-zone system, I highly recommend reading the newspapers from the week of November 18, 1883, that being the day the United States introduced its standard time zones.

Excerpt from "The Memphis Daily Appeal", Saturday, November 17, 1883:

Mr. D. W. C. Roland, general superintendent of transportation of the Louisville and Nashville Railroad Company, has issued a circular instructing "all hands" on that road that on Sunday, November 18th, at 10 o'clock a.m., the standard time of all divisions of this road will be changed from the present standard, Louisville time, to the new standard, ninetieth meridian or central time, which will be 18 minutes slower than the present standard time. At precisely that hour, by the present standard time, all trains and engines, including switch-engines, must come to a standstill for 18 minutes, wherever they may be, and all watches and clocks of all employees must be turned back 18 minutes, which will be the new standard time. Other instructions are given in the circular with regard to the manner of adopting the new system of time not necessary here to print.

Excerpt from "The Evening Star" (Washington, D.C.), Saturday, November 17, 1883:

PUT THE CLOCK FORWARD.
The New Time Standard to Become Effective To-morrow.
What Will Be Done in Washington.

To-morrow the public at large not dependent for their supply of time upon the "time ball" at the observatory will begin to regulate their affairs upon the new time standard, giving Washington the time of the 75th meridian, which is 8 minutes and 12 seconds faster than the real time of Washington, as registered by the daily transit of the sun over our meridian. Towns that have never laid claim to a meridian will have no embarrassment in effecting a change of time, but in this city, as the meridian is recognized as a government institution, according to the recent rulings, the actual Washington meridian time will continue to be the official time.

THE RAILROADS.
"It won't disturb us a particle," said Superintendent Sharpe, of the Baltimore and Potomac road, to a STAR reporter this morning; "as a matter of fact it will not disturb any railroad. The time is easily enough arranged." "Then the new time will go into effect 'on time' to-morrow," said the reporter.
"Yes, promptly at twelve o'clock," said Mr. Sharpe.
"I should think that it would cause confusion at first," said the reporter.
"It will cause confusion may be for the public," said Mr. Sharpe, "but as a matter of fact it will make very little difference on our road. We have always run by Philadelphia time, and this new standard makes a difference of only one minute and three seconds. Heretofore when we advertised a train to leave at 11 o'clock it left really at 11.07, according to Washington time."
The change on the Baltimore & Ohio road will go into effect at 2 o'clock to-morrow morning, at which time the new schedule recently adopted will become operative. It is thought that by making the change at 2 o'clock Sunday morning, an hour when there are few trains running, there will be little confusion.

THE BANKS.
A bank official, talking to a STAR reporter to-day, said that there had been no agreement as to the time to be employed in banking business. As a matter of fact, it would make little difference, as a margin was always allowed to cover any discrepancy in the clocks.

THE JEWELERS OF THE CITY,
who are the dispensers of time for the majority of people, will, as a rule, keep both times, so that their patrons can take their choice. Arrangements have been made so that the observatory will send both times to the jewelers.
Messrs. Galt, Brother & Co. will, on to-morrow, at noon, set the large clock in front of their building to the time of the 75th meridian. Their regulator inside, which is connected by wire with the U.S. observatory, will, as heretofore, show the time of the meridian of Washington. Mr. M. W. Galt said to a STAR reporter that he thought that the new time would necessarily prevail in the general course of business, as the railroads and the post office would be regulated by that time. As the new time is faster than the old, no one will be late, if they regulate their movements by it.
Mr. Karr, the jeweler, stated to a STAR reporter that whatever time the Observatory furnished would be supplied by the jewelers who had electric connection with the Observatory. He is having a dial with two rows of figures made for the large clock in his window, so that it will give both times. Some of the jewelers of the city are in favor of holding a meeting to arrange for the adoption of one time or the other throughout the city. The majority have decided to keep both times. Samuel Lewis' Sons are the only ones who have positively declared in favor of the new time exclusively.

THE CITY BELLS.
There was some doubt at fire alarm headquarters this morning as to what time the bells would announce to the public hereafter. As usual, on Sundays, the bells will not ring at noon to-morrow, but will ring at 6 p.m., which will be the first time the bells will tell the time after the new standard goes into effect. An official of the observatory visited the office this afternoon and stated that the old Washington time would be rung on the bells. This is in accordance with the instructions of the Secretary of the Navy. The matter, it is stated, was made the subject of Cabinet consideration yesterday. Circulars sent out from the observatory to-day explained the system of time signals, and said that Washington time would be sent from the observatory. The difference between Washington time and the 75th meridian time is stated in the circular.

Sir Sandford Fleming invented Worldwide Standard Time between 1876 and 1879:

After missing a train in 1876 in Ireland because its printed schedule listed p.m. instead of a.m., he proposed a single 24-hour clock for the entire world, located at the centre of the Earth, not linked to any surface meridian. At a meeting of the Royal Canadian Institute, on February 8, 1879, he linked it to the anti-meridian of Greenwich (now 180°). He suggested that standard time zones could be used locally, but they were subordinate to his single world time, which he called Cosmic Time. He continued to promote his system at major international conferences including the International Meridian Conference of 1884. That conference accepted a different version of Universal Time but refused to accept his zones, stating that they were a local issue outside its purview. Nevertheless, by 1929, all major countries in the world had accepted time zones.

Update:

Further research finds that New Zealand adopted a colony-wide standard time, based on the longitude of 175.5 degrees East of Greenwich, on Nov. 2, 1868.

Dr. Hector, in selecting the country's mean longitude (172 degrees, 30 minutes) as a basis for calculating a standard time, adopted what may now seem a very obvious course. But the fact remains that he gave a lead to the world, for no other country until something like fifteen years later adopted the same method for the calculation of its standard time. ....

..., but by the beginning of 1870, the work of the time service was begun, having been carried on continuously ever since by the Dominion (formerly the Hector) Observatory.