The Eastern Front was absolutely massive, and spanned four years. The answer to your question is highly dependent upon the time and place in question. Tactics used by both sides evolved (or devolved, in some cases) constantly throughout the war. Even the differences of strategy of the two sides is too big of a creature to give a meaningful answer.

I adore this site and highly recommend you check it out. It gives a great outline of what I believe it is you are looking for. From there you can refine your questions to something more manageable.

EDIT: Just want to add that the sections of the site you'd find most relevant are the "Germany Army" link as well as pretty much everything in the "Infantry Tactics" link. I was under the impression that he had a link for the Soviet Union as well, but it appears everything I recall about the Soviets he covers under the "Infantry Tactics" section, so read that part closely to get information about Soviet tactics.