Media typically depicts 17th C - Napoleonic Era line infantry as standing shoulder-to-shoulder in an open field and blasting devastating volleys at each other while stoically closing ranks as their comrades fall. Inevitably, they charge each other simultaneously, resulting in a decisive victory. Even historical accounts tend to bias decisive victories. How accurate are these depictions?
One would tend to think that human nature would be to take cover when being fired upon would be to "hit the deck" or run for your life. How were soldiers trained to maintain discipline as they were being slaughtered? What kind of tactics were used on the platoon level? How were casualties managed in the heat of battle?
So I mainly do 18th century history, particularly French and Indian War and the American War for Independence. Some of the earlier and later periods may be similar in approach but I'm sure there are some differences. This is a sort of quick answer.
The name of the game was discipline. When not marching on or on fatigue, NCOs and officers drilled the soldiers. After sometime of steady training, the manual of exercise (your loading, firing, and marching procedures) would become second nature. You also have to keep in mind that the sergeants were there to keep the men in line and in order. If a soldier fell, someone would simply close ranks and fill in that gap. Desertion from battle likely meant your own death by your superiors.
Maintaining discipline could make or break an army in battle. At the battle of Camden during the American War for Independence, the fresh Virginia and North Carolina militia broke and routed to a bayonet charge from the British 33rd. The line collapsed from there on and Gates lost the battle.
Also keep in mind that line warfare was not quite as deadly as might be depicted in movies or games. Yes, they are firing massive walls of lead down at the other poor bastards on the other side, but you're not going to see a whole regiment get obliterated in a single volley unless they're super up close. A line would be firing somewhere between 50-80 yards away. Any closer will becoming closing distance for a bayonet. Here's a nifty blog detailing some of the casualties from mid-eighteenth century battles. It is well written and researched, done by a graduate student I believe, who also does wargaming and reenacting. Anyway, the main goal wasn't to annihilate the other army but break them. Hammer them down, lower their morale, and then when they're faltering you run then down with cavalry or bayonet.
During the AWI both armies fought a bit differently than the tactics seen on the European continent. The British adopted light infantry style tactics. The open order meant more space in between each soldier and lessened the amount of casualties. Matthew Spring's With Zeal and Bayonets Only describes this adaptation. Light infantry fighting was faster and more mobile. You'd skirmish and harass the enemy line and then move back. There are also accounts of soldiers laying on their arms, sort of ducking for cover like you mentioned.
As suicidal as it might look to us, military tacticians back then were no idiots. They had a method to their madness. Linear warfare was the best way to operate armies of musketmen. It allowed for orderly marching and placement of troops. Having soldiers march and fire like clockwork made for optimal fighting as it allowed officers to move regiments and companies about as needed while keeping order. The formations also allowed the big numbers to act as not only protection from cavalry but also the ability to fire mass volleys instead of peppering with independent firing. A British soldier optimally could load and fire around 3 times a minute. It is a fairly long process to load and fire, and combine that with minutes of battle and smoke, it is not going to be devastating.
I hope this helps to answer your question. What exactly went on in the minds of soldiers at that time we can only guess. They were expected to be disciplined but of course, that isn't always the case. They were humans, not robots.
If it is any credit, I do AWI reenacting and study this time period. Currently a grad student.
Some sources and books that might be of interest:
Don Hagist: British Soldiers, American War
Matthew Spring: With Zeal and With Bayonets Only
You might also want to check out the journals of Joseph Plumb Martin and Roger Lamb. They're firsthand accounts from soldiers during the AWI and really informative of the lives of soldiers.