The order of the battle, in elements (meaning regiments for infantry, batteries for artillery, individual ships for fleet squadron) can be seen when you buy a unit (which is made of these elements), see the list of NATO symbol at the bottom of the screen.
When you get the unit on map, the elements will also be seen, but can't be manipulated directly. You manipulate units, eg the 7th Brigade (Virginia), made of 4-7 elements of various sorts.
If you have a divisional HQ around (which is also a unit and has to be bought) you can combine up to 18 elements with the HQ, and get a division.
The thing to understand is that you play with units, brigades and divisions mostly (but a unit can be made of a single regiment, so the unit is then also a regiment, like an independent Zouave regiment, you follow me?). There is a big tutorial on that, rest assured.
Take a look at the screens below:

Hoke's Brigade is a unit (selected as there is a the metal frame around it) and is made of 4 elements (see theses elements in the bottom right panel).
Now I have a HQ unit in the stack, so I can merge all the units into a single one: a formed division. After the operation I will have only a single unit to play with, but a darn potent one. I can always split it back into its components units.
See:

When you pass the mouse over Early's Division, you get a tooltip telling you what are the brigades into it, and you also the see the combined units (as a pop-up only). Now if you look to the right, you see the complete (and impressive) order of battle of the unit, with Jubal Early at its head.
A division is a very potent force, as you have added bonuses compared to having the units split. On the other hand you act as a single force and are a less versatile if you want to do several operations in a single turn.
It can appears daunting, as there is much info displayed (and you have many regiments), but it plays really smoothly on the contrary. A corps is made of 4-5 units most of the time: 2 divisions and some assets (supply or independent artilleries), so you are not overloaded with units, even if you have a bunch of troops under your command. And you just manipulate these units, the sub-elements are here to provide historical accuracy and background, and also serves so that the combat engine run realistic result, with many subtleties running underground. For example your division is perhaps only a single counter when you manipulate it, but the battle engine will use the artillery batteries in it to support the regiments, and the cavalry will also have the role of shielding you from losses if you retreat, etc. Even better if you have a sharpshooter company in the division, all the regiments of the said division will benefits from the special ability he has (increased initiative).