In terms of tactics, perhaps the most important one for modern warfare is on infantry tactics the Germans developed in the latter half of WW1.
1. Machine gun: The Germans were the first one to treat machine guns as the basis of platoon level tactics. Reasons: a) Machine guns provided the bulk of firepower, compared to other small arms available in a platoon; b) Riflemen's job was to protect their machine gunners. In addition, they positioned their machine guns in such a way as to maximize crossfires and when they did open fire, they struck obliquely at advancing opponents. They also frequently changed their machine gun positions.
2. Infantry assault: They relied on shorter but more intense artillery bombardment, followed by well-equipped infantry and engineer. Their job was to disrupt enemy's line and bypass strongpoints; follow-up troops were responsible for reducing strongpoints.
3. WW2: The basis of infantry tactics were already developed by the end of WW1. So, add on refinements in WW2: a) Light machine gun -- the most infamous example would be MG-42, but what made it particularly lethal was its high rate of fire and its barrel was easily replaced; b) Motorized infantry -- they made sure to have their tanks supported by motorized infantry, engineers and artillery; c) Small unit leadership: They paid attention to the training of their NCOs and junior officers, which then allowed them to issue mission-oriented combat orders (you are given objectives, but it is up to you and your subordinates to figure out how to go about), making them tactically more flexible than most of their opponents.