No matter how well you plan and execute your attacks and defenses, you will inevitably wind up in a fire-fight at a battle. I categorize a fire-fight as a shooting match between to non-moving forces. But, in the definition of a fire-fight, we find the solution to solving the problems presented when two forces pin each other down with fire. That is, namely, movement.
The average WWII reenactor moves relatively little. This is reflected at battle reenactments as you will often see reenactors that will pick a fighting position and stick with it until he is dug out or killed. To counter this unfortunate reenacting trait, the enterprising gruppenfuhrer can overcome an enemy in a fire-fight by simply instilling the principles of movement and initiative. These principles can most easily be brought to out of the citizen-reenactor during training sessions before events (more on traing in future.)
When your squad is in a fire-fight however, do not assume the you have done somthing wrong. A fire-fight can spring up from any meeting engagement, but is usually the result of an improper defense. In many cases the defending squad chooses sufficient cover, but fails to utilize good fields of fire (schussfelden.) The net result is that the defenders can hold their position but can not inflict serious casualties. note: you will know quickly whether or not the enemy is able to inflict serious casualties. At this point, your squad will (if it has reflexes better than your grandmother's) instinctively go to ground. Now, with both sides pinned, a fire-fight ensues.
The first principle that will lead you to victory is initiative. Your men must be always looking for ways to put a real pinch on the enemy. In this case, merely shooting at him from your cover, or concealment, is not initiative. Initiative is finding a good field of fire that threatens many of the enemy's positions. Also, initiative may entail a reenactor finding a succession of positions that give good fields of fire on a number of enemy positions. The reenactor that is always looking for a better way to get at his foe has initiative and will more often than not be victorious.
In order "get at them" the reenactor with initiative must employ movement. The only way to win is to move. He who sits still in a fire-fight is lost. One of the best ways for a soldier to move is onto the enemy's flank. In this case, unlike in the advance, stealth is not as important as in the advance since the fire will help conceal your movements from the enemy. The trick to moving is simply to keep bounding from cover to cover while working towards a good position. This helps do many things. It will often confuse the enemy as to your actual strength. It also unnerves the enemy when they see that your squad has more verve than they do. Movement does not necessarily mean advancing, though. You can also use the fire-fight for setting up a defense and/or ambush. The key is to move, somewhere, and have a plan about it. Don't be afraid to be aggressive.
Another important element about the fire-fight is the volume-of-fire approach. I have been in too many fire-fights where it has gone dead silent for moments on end. This often leads me to wonder whether this is really combat, or a pocket-protector convention where every nerd is afraid to speak. It is as important in the fire-fight as at any time to always be firing at the enemy. For this the squad leader must (again, as always) assess his weapons. The good thing about the fire-fight is that the squad leader has great freedom when it comes to weapons. If the squad has grenades, structure a fight around the grenadiers. If an MG is present, use that to benefit the rest of the squad, etc. Remember, never stop fighting.