I read in Anthony Tucker-Jones's T-34 The Red Army's Legendary Medium Tank (2015) that:
Although he consigned the Red Army’s tanks to an infantry support role (which spelt disaster in 1941), he at least helped provide a tank that would ensure final victory.
But from what I understand from other places, the US used the Sherman mostly in the infantry support role to great effect.
I know that heavy tanks are best used for breakthroughs (with the exception of the British infantry tanks), but what was the best way to use a medium tank?
The US Army used the M4 in two roles: Infantry support, and exploitation. The hole in the enemy's front line was supposed to be punched by the infantry division, (or held in defense by) and the armored division was the one which was going to play merry hell in open maneuver. The same tank was used for both types of unit. Thus, depending on if your tank was an independent battalion (which were attached to infantry divisions) or part of an armored division, your operational 'role' was set up accordingly. The tank was identical in both cases, and well capable of doing both. What it wasn't capable of was shrugging off defending fire, such as the heavy tank would.
In the US Army, initially the light tank was actually the one tasked with infantry support. If you look up the US Army's FM 17-10, for example, the Armored Force manual, it stated that the job of the light tank is the support the attack, and the job of the medium tank is to protect the light tank. Over time, of course, the battlefield became far to dangerous for light tanks to stay in the line, and the Mediums took up much more of the primary role in the support of the attack.