Question: In the 19th century, do we know how armor changed with respect to guns of the time? ..... it very hard for me to get a general idea of warfare during this time.
Beginning in the late 1400's guns made armor more prevalent on the battle field. Not just knights, heavy calvary or nobles but common infantry would fight in heavy plate. This necessitated armor becoming cheaper, less decorative, made from standard interchangeable components to bring down costs. Rather than being custom made for an individual it was produced in bulk and stockpiled to be used by by common soldiers. This was called munition armor, or munition grade armor. By the end of the 17th century as firearms tactics and the weapons themselves improved all forms of defense including personal armor for infantry to became devalued. Troops were drilled to concentrate their fire and to stay in formation as they marched into range of enemy formations which were doing the same, all without armor or protection. Napoleon in the early 19th century exemplified this philosophy as he always chose to be on the offensive. Military doctrine was one which valued offensive action. Offense had so many advantages it was believed that all defense was counter productive. Anything which did not contribute to offense or encumbered a unit's offensive potential was abandoned. Body armor for infantry would thus not be used in the 18th to the early 20th century.
Some Plate or heavy armor for Calvary lasted into early 20th century. Cuirassier, a form of heavy cavalry which used Curas Armour. The breast and back armour without the arms or visor. This form of heavy cavalry was still in use and saw action early in WWI. It was really more of an exception though, most cavalry chose the increased mobility and versatility of fighting unarmored.
French 6th Cuirassier Regiment in 1887.
The first European battle in which firearms played a decisive role was the Battle of Cerignola
(1503) between Spain and France and the weapon used was called the arquebus
Battle of Cerignola
... one of the first European battles won by gunpowder weapons, as the assault by Swiss pikemen and French cavalry was shattered by the fire of Spanish arquebusiers behind a ditch.
Plate armor coexisted with firearms on the battlefield, up until the mid 1600s. Plate armor (breast plates) was routinely tested against fire arms by the armorers. The dent from the bullet being engraved to draw attention to it as a demonstration of the armor's quality and effectiveness. This was called proof testing or just proofing. Leeding to the expression bullet proof.
As a low-velocity firearm, the arquebus was used against enemies who were often partially or fully protected by steel-plate armor. Plate armor worn upon the torso was standard in European combat from about 1400 until the middle of the 17th century. Good suits of plate would usually stop an arquebus ball at long range. It was a common practice to "proof" (test) armor by firing a pistol or arquebus at a new breastplate. The small dent would be circled by engraving to call attention to it. However, at close range, it was possible to pierce even heavy cavalry armor, although penetration is heavily dependent on the power of the arquebus and the quality of the armor.
Japanese cuirass with bullet marks from being tested for resistance to firearms.
With the introduction of Firearms, Armor got more prevalent on the battlefield. In the prior age of knights armor was custom made, intricate, highly personalized, decorative, made of steel and highly expensive. It was used by nobility. In the age of guns munition armor(heavy plate) was manufactured to be less expensive. It was made from standard patterns, interchangeable parts and often made of inferior metals like iron rather than expensive steel. Munition armor was made to be stock piled for use by common soldiers.
Early Modern Warfare
Since a firearm requires little training to operate, a peasant with a gun could now undermine the order and respect maintained by mounted cavalry in Europe and their Eastern equivalents. Although well-smithed plate-armour could still prevent the penetration of gunpowder-weapons, by 1690 it had become no match for massed firearms in a frontal attack and its use ended, even among the cavalry. By the end of the 17th century, soldiers in the infantry and most cavalry units alike preferred the higher mobility of being completely unarmoured to the slight protection - but greatly lessened mobility - offered by wearing plate armour
Innovations like volley fire signaled the end of infantry armor. Especially so when firearms improved with more reliable firing mechanisms (firing pins/flint locks), greater accuracy and longer range(rifles).
In the early 19th century, Napoleon demonstrated the value of maneuverability, coordination, and offense action, in the age of firearms. Napoleon always chose to attack rather than defend and this became an unquestionable doctrine for military theorists in the 19th and early 20th century, an age mostly devoid of personal armor.
The Emperor preferred to fight offensively under all circumstances, even when on the defensive. At Austerlitz he did actually stand on the defensive, lured his enemies into a trap, and then attacked.
"No one should imagine that sound heads are common in armies.
Offensive generals are rare among us; I know only few, and,
nevertheless, it is only to these that ... a detachment can be
entrusted." - Frederick the Great
For those who came after Napoleon, all forms of defense became devalued. It was believed that so overwhelming was the advantage of troops on the offensive, that anything defensive in nature was counter productive and would cost lives. The culmination of this became known as the cult of offense among military theorists, which was influential until WWI.
Heavy body armor in some Calvary lasted into the 20th century. As heavy Calvary gave up lances and adopted firearms the knights were replaced in the 19th century by Cuirassier, a form of heavy cavalry which used Curas Armour. The breast plate and back armor without the arms or visor. This form of heavy Calvary was still in use and saw action early in WWI.