We know that the Spanish Armada was composed of over 200 ships. How did the Duke of Medina exercise any sort of control over a fleet this big with only 16th century technology? Do we know how the ships passed commands to each other and anything about how it was organised? Did this command structure contribute to the eventual shipwrecking of the majority of the fleet?
There's very little concrete evidence about how command and control of the Spanish Armada worked, or indeed, how naval tactical control was exerted during that period, which pre-dates what we now call the Age of Sail.
Most of the documentation that has survived from the Armada is correspondence that is essentially at the political level, i.e. between the King and his commanders. So we know at a strategic level who said what and when but don't know in any detail how, and if, these orders were transmitted down the chain of command.
We do know that the Duke of Medina Sidonia wasn't a naval man whereas his second in command, Juan Martínez de Recalde was an experienced Admiral in the Spanish Navy. This lead to some friction between the two because the Duke insisted on sticking to King Philip's plan of attack, while de Recalde would have prefered to have dealt with the English fleet (especially when the opportunity arose to attack them in the Solent).
At the time of the Armada, the standing national navies of the European states were quite small and there were few professional naval officers. As can be seen from the make up of both the Spanish and English fleets, the actual number of warships on both sides is dwarfed by the number of armed merchants and transport ships.
This greatly limited the tactical options available to both sides. Even relatively simple fleet maneuvers require coordination and practice to pass off without incident. Trying anything too complicated when most of your ships have little or no fleet experience is risking collisions or worse.
So what methods were available to pass orders?
In person - The subordinate officers could meet the commander on his ship to receive orders. This allowed commanders to discuss strategy and tactics at a detailed level more quickly than would have been possible with any other method.
Written instructions - These could be strategic communications, passed by despatch boats back to Spain and ahead to the Duke of Palma, or tactical communications within the fleet passed by ship's boat. These were most useful for passing more complicated orders than flags, guns or lights could transmit.
Flags - While this seems an obvious method, it must be remembered that there was nothing like the signal codes and fighting instructions that were common to the professional navies of the late 17th and 18th Centuries. Flag signals would have been limited to pre-arranged orders such as "attack", "withdraw", "follow me", "anchor here", etc.
Guns - Signal guns used in much the same way as flags to pass pre-arranged orders. They had the advantage of being useful at night or in poor visibility but were, obviously, of little use during a battle.
Shouting - Orders could passed ship to ship by voice when they were close enough. This could also be used when sending a boat between ships to avoid any tricky transfer between boat and ship. While this method was limited in range, it did allow for more complex orders to be passed.
Lights - Useful at night but even more limited than flags and guns in passing orders.
Did the problems of tactical control contribute to the failure of the operation and the loss of ships on the return? Certainly control over the fleet was never fully re-established following the flight from Calais but bad luck and poor navigation played a larger part in its losses.
It was never part of the plan for the fleet to sail around the British Isles to return, so I'd imagine that the maps available for that part were more rudimentary. By the time they reached the open waters of the Atlantic many of the ships were in poor condition and were barely sea worthy. The relatively primitive navigation aids of the period meant that they failed to establish their position accurately. As a result, they ended up turning south far too close to the British isles. This, combined with unusually bad weather, lead to a large number of losses on the Scottish and Irish coasts.
ref: Naval Warfare in the Age of Sail, Brian Tunstall (Conway, 1990)
Fighting Instructions, 1530-1816, Sir Julian Corbett (NRS, 1905)
For manoeuvres, like Pieter said: flags and horns. Lanterns at night for guiding purposes – as seen here, resulting in a scattered English fleet when Drake snuffed it for more discretion – rather than as a means of communications. (Use of optical telegraphy is speculative.)
As to whether or how the command structure contributed to fleet's destruction, I've honestly no idea. But as I understood things, the 1588 armada was primarily defeated by superior English manoeuvrability, superior English seamanship, and unusually strong North Atlantic storms. There admittedly were some issues related to communications (e.g. awaiting the Duke of Parma in a fixed rendezvous point, communications taking time), but none seemed attention-worthy.
The Manchu Dynasty used flags to coordinate their massive Armies which conquered all of China in and around 1600. Since the Portuguese had already sailed as far by then it is interesting to speculate that Europe had developed an advanced system of "flagging techniques" prior to the Manchu...and perhaps used in this engagement which lasted for some time. (Weeks? A month?) The most obvious way to communicate is through a written order committed to memory then discarded (burned) then there would be no record of any communication system being employed. That would appear to be the case here. In other words "verbal commands" literally given in person on the Commander's ship to the Commander personally. After the failure to land at London a "frag order" or change of command would have to have been given in this instance since it made no sense for the Armada to sail North around Scotland then West into the Irish Sea which ultimately doomed the Fleet. Great Britain did attempt a counter offensive by landing in Lisbon, Portugal...but this was a disaster for Great Britain as well. After that "flagging your vessel" became a signature item for maritime law and seamanship. The most valuable possession on board a ship after the Spanish Armada was usually the bill of lading. That, a sextant and a "map" was about all that a sailor needed to "go exploring." Having familiarity with the terrain was of great advantage to the European Powers for centuries as outside of the later United States and Canada there were no "shipping powers" in the New World save for maybe the Maya. That's true in the Americas even today actually. This is certainly not true in East Asia anymore though.
First of all, the man that was elected to command was Alvaro de Bazan one of the most skilled and prestigious admiral in Spanish History. This admiral son of Basques as his father´´ he became an admiral of the Spanish navy. In other words, the best man to lead an invasion England with experience against French and Turkish navies with great victories. He maid even an expedition plan very well prepared, however, he died a month before the plan was completed.
Was known that even Alvaro, the admiral, told Philip II that he needed more time to prepare fleet something that the king saw badly and pressured him to finish as soon as possible.
After, the died of the veteran admiral, the Spanish navy received a very bad news because he didn't have any other admiral to lead the fleet. Only the skillful captains in many warships.
Phillip decided for Duke Medina Sidonia, a man with few skillful in Italy as a land officer. Even, the duke tell the king that he was not the right man to command due to his non-experience at the sea, even he didn't like the sea.
Did you imagine a general commanding a fleet?
Spain will not a have a good admiral in the fleet until XVIIIth century. Philip was forced to use the captains with his warships without using a large scale group of ships. Something that have temporary success like the sack of Cornwall and many others.
In the imperial Spain, was necessary to have a good fleet in order to transport the tercios the finest army of those years.
Many times tried to invade England but always the plan failed due to the storms.
In the early XVIII. century, with the fleet rebuilt and with good naval officers tried to defy English power. Even was near to get success. Spain planned a rebellion of Scotland having his heir protected by strong 300 Spanish soldiers. The first part of plan was achieved, however, the second part of the plan failed. this second part was an invasion of west England with Spanish fleet transporting an strong Spanish Division with admonition and weapons for 3 divisions (in order to join volunteers in whole British islands) in order to invade England. However, due that the Atlantic oceans had strong storms the Spanish admiral decided to stay at the Spanish port provoking the delay of the mission. At the England only fought against Scotland and the 300 Spanish soldiers abandoned.
Later, after Napoleon invade Spain having his navy and army under his control forced them to join the fleet with France fleet against the royal navy provoking the destruction of the complete Spanish fleet.