Also if I can be recommended any books on the Prussians, with emphasis on their military history that'd be great, but any book regarding them is welcome all the same!
Basically, the Prussians had professionalism and really good marketing on their side, and that led to a belief - not entirely justified - that they were superior soldiers.
In the 18th century, it's important to remember that most professional armies, be they French, Swedish, British or Spanish, were technologically equivalent to one another. Smoothbore muskets and bayonets were the standard arm for infantry, carbines and sabers - some lances and spears - were standard for cavalry, and artillery had a maximum field range in most cases of no more than a mile. Psychologically, this cannot be underestimated. It meant that, in the standard cliche of an open-field battle, one would be able to see their enemy advancing for much longer than you could possibly do anything about it.
This essentially boils down into a couple of important points. One; flashy uniforms that stand out are better. It's axiomatic among people who don't actually study the era that brightly colored uniforms are stupid because they stand out, but that's precisely the point. Tall hats like grenadiers mitres, uniforms that emphasize shoulder width, brightly polished steel on the musket and shined crossbelts all give the effect of uniformity and discipline. And two; discipline, discipline, discipline. You want the enemy to see you coming, you want your soldiers to advance regularly, and in-step if possible, because there was nothing considered more demoralizing than a perfect, seamless, disciplined advance. The more regular and drilled the advance looks, the more possibly demoralizing it was. The better you march, the better you're trained. The better you're trained, the faster you can fire your musket. And if your side can fire faster than the other side, it's much more likely that the slower side will break and run sooner, which was the ideal. Bayonet charges could decide things extremely quickly as well, since most soldiers would break and run before it ever came to fighting with them. Most nations used a big, triangular wedge between 12 and 16 inches long, a wound with one of those was terrible, and everyone knew it. You'd hotfoot it out of there if you could.
So, the side that appears more professional has an edge, even before firing starts. And this is primarily what the Prussians took advantage of. They were considered more professional. They made themselves the world standard, because of some complicated politics covered in some of the links posted by /u/Searocksandtrees, which manifested in a standing, professional army.
This army not only had a distinct advantage over, say, the British, who tended to de-militarize after major conflicts and kept a very small army in peacetime, on the simple basis that they were professionals, but also because they had a proud tradition. Frederick William, the reformer who made the major social changes in Prussian society during and just after the 30 Year's War, laid the groundwork for Frederick the Great, who gave Prussian soldiers a winning history and did much of the work to give them their fearsome reputation.
The Prussians made it a point to demonstrate the efficacy of their army regularly. They invited heads of foreign armies to come to their maneuvers, which they held somewhat regularly, to see their crack units drill and fight mock battles. Some British advisors, seeing these maneuvers after the American War for Independence, claimed that Prussian soldiers could fire 6 shots in a minute (absurdly fast, but probably not terribly accurate or powerful, as they apparently skipped ramming), and marveled at how Prussian formations moved like clockwork. These maneuvers, of course, were intended to have exactly that effect. They were held on ground that was prepared, that was drilled on again and again, and the maneuvers they showed off for other nations were more like parades, but the intent was to be as flashy and as impressive as possible.
Combat was an entirely different story, but what they were exceptional at was showing other nations that they were the experts, whether it was justified or not. It usually worked; the British were certainly impressed, and Americans hired a Prussian to drill American regulars in the War for Independence, et al.
tl;dr - the Prussians were masters of self-promotion, and understood the psychological effects of a well-drilled army core.
Richard Holmes' Redcoat covers the British army more so than the Prussian, but has a lot of the contextual information with regard to soldier psychology and battlefield conditions I used above.
Mark Urban's Fusiliers as well, which covers strictly the 23rd Rgt. of Foot through the American War of Independence, but has a chapter at the end covering the period between the end of the American War and the beginning of the wars with the French, and covers the British perspective of those Prussian maneuvers.
And Robert Citino's The German Way of War is a pretty thorough and well written account of the Prussian/German military tradition and history.
You will note from the links provided by /u/searocksandtrees that there are two major periods of Prussian military dominance. One under Frederick the Great in the 18^th Century explained by /u/PartyMoses here and the other under Helmut von Moltke in the mid to late 19^th Century. The links on this page will give you a good idea of tactics under von Moltke, but another important element was doctrine, especially in command and control.
After the death of Frederick the great the Prussian army found itself unable to adapt to a new form of warfare displayed by France under Napoleon. Frederick grounded his army in iron discipline and unquestioning obedience which worked because he was an extraordinary military genius and entirely capable of leading and directing battles personally. France’s post-revolutionary army however was a product of its citizens and hade a more egalitarian approach. Napoleon encouraged his generals to be flexible, split the Grand Armee into smaller, self-sufficient corps and relied on junior leaders to react to the battle as it unfolded in front of them. At the twin battles of Jena and Auerstedt in 1806 this French army defeated the Prussians decisively because it took the initiative and responded more quickly to changes in the battle; French commanders used their initiative, whilst the Prussians waited for direction form above.
The defeats of 1806 were a major culture shock for the Prussians and led to a generation long revision of their command doctrine. Carl von Clausewitz, who was present at Jena, was inspired to consider the nature of war and amongst many important theories he described the concept of friction:
In war everything is simple, but even the simplest things are difficult. These difficulties accumulate to produce a sort of friction which is unimaginable to those who have not experienced war.
Clausewitz is describing warfare in mechanical terms, but goes on to point out that an army cannot be a machine and war cannot be won through scientific analysis. The idea of war as a chaotic activity caught on and Helmut von Moltke seized on the idea to develop the doctrine of auftragstaktik, known in English as Mission Command. Von Moltke himself noted that:
..no plan of operations extends with any certainty beyond the first contact with the main hostile force.
And so the idea of auftragstaktik was to delegate responsibility to the lowest level possible. In the new Prussian Army no man would be punished for using his initiative, it was understood that no course of action could be perfect and so mistakes should be tolerated and personnel could even ignore direct orders. This last point lies at the heart of the Prussian command philosophy – a commander tells his subordinates what he wants them to achieve, not how he wants them to do it. The result was an army that could out-think its opponents, respond quicker to changes and thus maintain momentum. In the words of Sun Tzu:
Water shapes its course according to the nature of the ground over which it flows; the soldier works out his victory in relation to the foe he is facing.
The commitment to this philosophy is remarkable, during the Franco-Prussian War von Moltke shows none of the obsession over detail which might be expected. He shows little interest in troop dispositions, quantities of ammunition or other stores, or even casualties. His dispatches provide situational updates for his commanders, revised direction and occasional direct orders, but the detail is left to be sorted at the most appropriate level. For more information on Mission Command (a philosophy still widely debated in military circles) this paper by Stephen Bungay is excellent and includes a good example of a Prussian brigade commander, von der Goltz, disobeying a direct order in action leading up to the siege of Metz. It also considers the use of Mission Command since the 19^th Century including the German Army’s reforms in the 1930s.
hi! not discouraging any of our many military historians from chipping in on this one, but meanwhile, you may be interested on a few previous posts about the Prussian military, all of which include book refs