I may well be wrong, but from what I've been able to gather it seems like the Soviets believed that a defensive war was a sure way to lose, and built their army around constant, sustained attack.
I've also heard that they focused more on the strategic level than the tactical level, and Soviet officers and NCOs were given more flexibility to seize the initiative than their NATO counterparts.
Outside of very dry NATO field manuals I've not been able to find an awful lot of information on this topic, and it's something that really does interest me.
You are talking about Deep Battle, and you are correct. A Soviet attack would have consisted of tanks and motorized rifle divisions advancing deep into NATO areas. These spearheading forces would not engage the enemy unless they had to; the goal was to punch a deep hole through NATO lines before REFORGER units could be shipped from the United States. This was embodied in the Seven Days to the Rhine war plan leaked by the Polish government in 2005.
American doctrine, starting in 1982 had coalesced around AirLand Battle. AirLand was all about technology. The United States and NATO could not attempt to have numerical parity with the Warsaw Pact. This is where the M-1 Abrams, the A-10 Thunderbolt, the Ah-64 Apache, and the F-117 stealth fighter come from. Stealth fighters would be used to decapitate Warsaw Pact command and control and disable their air defense systems. With the Soviet AA suppressed, NATO could use F-15s and other fighters to establish air superiority, allowing A-10s Ah-64s and other assets to engage the Soviet armor in relative safety. This was a delaying action until REFORGER units could come from the United States. Casualties would be immense.
Needless to say, submarine warfare was hugely important as well. The soviets wanted to stop the REFORGER convoys, NATO wanted to protect them.
Sources:
THE EVOLUTION OF U.S. ARMY DOCTRINE: FROM ACTIVE DEFENSE TO AIRLAND BATTLE AND BEYOND, Long, Jeffery 1991
AIRLAND BATTLE DOCTRINE Skinner, Douglas, 1988
What I'd really like to learn is Soviet infantry doctrine, especially on the platoon sort of level. I have heard a Soviet infantryman carried far more grenades than his NATO equivalent, and combined with every man carrying an automatic rifle, I would imagine that even their infantry doctrine stressed constant attack.