There've been a lot of questions about WWII strategy over the years, but I'd recommend /u/vonadler's excellent answer in this thread. You've got a pretty broad question there, but this answer should cover most of what you want.

For that I recommend you read: "Achtung-Panzer! by Heinz Guderian"

He argued against "stationary tactics" like that of previous wars, where one could be easily bogged down and bled dry.

e.g.: Germany in world war I.

He envisioned grouping armor in large concentrations, supported heavily by the air force, and using them as the hammer of an offensive.

Previously the use of armour in vehicles was that of a troop support, but world war II tactics shifted to group armour into units. As seen in the early war, Germany rolled to swift victory using this tactic, championed by Guderian, while the Polish and French hadn't adopted the doctrine and continued to distribute their armor piecemeal to support infantry.

The radio played a huge factor in making this possible as the tanks could communicate amongst each other and with HQ/supporting air force. This was the real reason behind German tank dominance in the early war, contrary to what you usually hear which is "Germany's were the best in the world". To a large degree, especially during the Polish campaign, the German tanks were really nothing special in comparison with any other power in Europe.

This doctrine, or "Blitzkrieg" (Lightning Warfare in German), was when groups of armor units, supported by air units, were used to punch a whole in an enemy defensive line and then continue forward, leaving strong points for the following infantry to mop up. This disrupted enemy communications and spread panic as it often meant the German armor units would show up in places they weren't expected behind enemy lines, even the German High Command would lose track of them due to how fast they advanced. This also lead to the invention of the notorious "Stuka Dive Bomber" used to drop bombs on ground targets with astounding precision and equipped with a siren, that during a dive, screamed like a banshee.

As one German Officer under Guderian was quoted as saying: "We were told to push forward with no regard to anything to our left or right, simply forward at all times."

By the closing of hostilities, the USSR had adopted similar tactics. As well as on the western front by the allies, to a lesser degree.