I'm by no means an expert, but I've read somewhat on the subject and I'll attempt to give you a quick rundown. I know mostly about the organization of Infantry during this time, and can’t really offer you much about the organization of cavalry or artillery. So I’ll focus primarily on foot soldiers.

INFANTRY: Despite the famous exploits of the cavalry of any army, and the growing importance of quickly deployable and concentrated artillery, infantry still played the crucial role in Napoleonic Warfare of taking and holding ground, something the other two arms could not easily do without infantry support. The majority of the numbers in any given military force would of course be infantry.

The organization (and I'll use the British model because that's what you seem to be more curious about) was based more or less upon the battalion. A Battalion was commonly divided up into ten companies, and the company is usually the smallest dividable unit at the time (these were often broken into "fire-platoons" but only during general engagements, and not as an operational unit). Each company would have a full strength of 100 men, thus making the ideal strength of each battalion 1000 effectives. In reality this was extremely rare however, as the wear and tear of campaigns, battles, sieges, disease and other maladies tended to decrease numbers. In practice a typical company would have anywhere from 40-60 effectives, thus averaging about 400-600 men per battalion. In fact it became so rare to have a full strength battalion of 1000 men that Arthur Wellesley actually halved the number of troops needed to continue being a battalion, making it 500.

Battalions were part of a Regiment, and as I understand it each regiment would have around 1-2 battalions. Often the term is interchangeable because there would be one regimental battalion actually deployed while the other would be stationed in Britain and would function to train, equip and recruit troops to reinforce the deployed battalion.

Regiments (or battalions) would often be grouped together with 2-3 others to form a Brigade. Brigades thus would number anywhere from 1500-3000 troops, depending on the numbers in its constituent regiments. Brigades would be subsequently grouped with perhaps 1-2 other brigades to form a division, which could reach 4000-6000 effectives. Divisions could be further grouped, with other divisions and also with cavalry and artillery, to form Corps. However during the British involvement in the Napoleonic War, for instance in the Peninsular campaigns, their numbers rarely reached a number where this would be possible or efficient.

In terms of Infantry officers, as I said the smallest grouping of soldiers would be into companies, each commanded by a Captain. Under him would be 1-2 Lieutenants, as well as several Ensigns, or junior officers. These would form the officers of any given company. The entire Regiment would assumedly have then 10 captains, around 20 lieutenants and a body of junior officers as well. These are all theoretical numbers mind you, as at times certain officers would die or be promoted etc. and there would be different numbers of officers among the different companies. Above the Captains there would be 1-2 Majors, who saw to a lot of the management of the disparate companies. Above the Majors was the Colonel, who had command of the Regiment/Battalion. Thus from top to bottom you have: Colonel - 1 Major - 2 Captain - ~10 Lieutenant - ~20 Ensign - ~20-30

Further up the chain, you begin to have Generals. The lowest rank was a Brigadier General, who obviously commanded the aforementioned Brigade. Then came Major generals who would usually command a Division, and so up to the General of the actual army.

In the British army there was a breakdown between the companies themselves. 8 of the companies would be considered regular or 'center' companies. They would comprise the main line of battle. The first and last, or "flanking" companies would be composed of different troops. The first, or ‘Grenadier’ company, would be composed of larger, taller and stronger men than the others. They were particularly useful in close physical combat because of their strength and physical appearance. The last, or ‘Light’ company, would usually be composed of smaller, lighter and faster troops who were often picked out for their individuality and intelligence. They were tasked with spreading out in "skirmish order" in front of the line of battle, to harass the enemy line with irregular fire as well as shield their comrades from enemy skirmishers. The two flanking companies were at times combined to create elite units for special tasks, such as the taking of breaches. At times entire brigades or divisions were created with this in mind, and these groups were considered to have a certain élan when compared to other bodies.

Hope that was helpful! The person above me listed probably the best sources to find this stuff out,and I’ll just re cite them.

Haythornthwaite, Philip J. The Armies of Wellington. London: Arms and Armour, 1994.

Reid, Stuart, and Duncan Anderson. Wellington's Army in the Peninsula, 1809-14. Oxford: Osprey, 2004.

On another note, if you enjoy well-researched historical fiction, then the Sharpe series by Bernard Cornwell do a relatively good job of recreating the time period of the Napoleonic wars as well as portraying and explaining the idiosyncrasies of the British military system at the time. Quite a lot of artistic license so I wouldn’t use it if you are just looking for the facts but interested nonetheless!

Are you asking about the army's hierarchy specifically, or the formations used and the deployment of soldiers?