This issue (like a lot with the color guards) comes from various and scattered pieces from several manuals. I won't be able to give many detailed sources for this area, but I can tell you how they work in practice on the reenactment field.
First of all, dressing to the right is what is done on the individual company level, when that company is alone and not in the battalion line of battle. Once the battalion is formed, the dress will be to wherever the battalion commander orders it (this will almost always be to the colors/center, though there are a few exceptions). Assuming the battalion is moving straight forward in line of battle, the dress for the right wing of the battalion (1st-color companies in a 10 company battalion) will be dressing to their left (on the colors). The left wing of the battalion (6th-10th companies) will be dressing toward their right (again on the colors). If the battalion was in a column of companies (1st company leading the battalion) then all of the companies would be aligned on the march by their left flanks (dress for the column set by the Right General Guide and 2nd Sgts. of every company). By staying dressed by the left of each company it will hep preserve the companies' wheeling distances and positions within the line for most if not all maneuvers where they need to be brought back into a battalion line of battle. If the 10th company was leading the battalion (moving the battalion to the left instead of the right as in the above example), then the principle would be reversed (i.e. companies dressing by their right flanks on the Left General Guide and the companies' 1st Sgts.
The reason why the dress might change in line of battle has to do with bringing your companies into and setting the direction of the line if they have been on the march and moving in column. Let me demonstrate this with an example of a battalion in close column of companies with the 10th Company (left flank) in the lead. The order of march for the column would appear as follows... (&=colors, C=color company...due to computer formatting this companies might not appear it here, but they should be aligned on their right flanks, but not necessarily on the left due to different company sizes)
---10--
--------
----9---
--------
---8----
--------
---7----
--------
---6----
--------
&--C----
--------
---5----
--------
---4----
--------
---3----
--------
---2----
--------
---1----
--------
Let us say the battalion commander want to form a line of battle directly in front of where the unit is marching, and facing the same direction as the line of march. The command for this should be BATTALION, Forward Into Line! By doing this, the unit will basically peel the companies out of column and back into line in their proper positions (since in this case the 10th Company is in the lead, it will take its place in the line after marching 6 more paces, then halt, and serve as the basis for the line to form). This means that the 10th Company/Battalion's left flank will become a fixed point. As each company comes into line they will need to quickly dress to the left (conforming to the 10th Company) and then prepare to open fire (if engaged). (Below, "........." are only used as place holders for the computer)
---10---
-------- ---9----
.............--------
........................---8----
........................--------
etc... Reverse of this if 1st Company leads and the battalion forms to its left.
Once the battalion line is formed, the dress would shift back to the center/colors.
--------------------------------------&-------------------------------------------
----------------------------------------------------------------------------------
Long examples for not answering the question yet, but knowing where the guide/dress is will be essential when figuring out how to adjust the line for casualties. Generally speaking, on the field it is essential that a unit occupies the maximum frontage that it can effectively hold. As a fight goes on you lose more men and your unit begins to have its front shrink...you want it to shrink grudgingly and as gradually as possible. It is also important that the companies keep from getting mixed into one another and remain effective for further maneuvers. (I.e. each company may start with different numbers of men, occupy a different frontage in the line, and lose men at differing rates). Let's look at 3 companies in line before and after casualties...(&=colors, S=1st Sgt, l/r=left/right of a company's rear rank to mark where units end and begin, "..." are place holders).
Before
----3---S&---2---S----1---S
l--------r l--------r l--------r
After (2d Company takes casualties, but not 1st or 3rd, dress is to the center).
----3---S&-2-S----1---S
...l--------rl--rl--------r
As you can see, the rear ranks have become jumbled and companies are overlapping each other, becomes much more apparent with hundreds of men. Even more of a problem is that now most/all of the rear rank has uncovered their original file partners, which will put a number of men in the rear rank that are now shorter than the man directly in front of them (this is all because of how the companies form based on height...another complex topic for another day).
The way to combat these problems, keep the front as wide as possible for as long as possible, and yet keep it easy enough to enact while under fire can be done in 2 steps.
1. If a front rank man is hit (now out of the line/no longer fighting), the rear rank man behind him steps up and takes his place in line. If a rear rank man is hit, nothing needs to be done.
C----CC----CC----CC----CS
---- ---- --------- --- ----
2. If a file is now vacant (the front and rear rank man have been hit), the file next to it will dress to the center (right or left depending on the company's position in the battalion line). For the above company let's assume it is 1st Co. and so its dress is to the left.
C--- CC ---CC--- CC- --CS
---- --- ------ -- ---- -----
becomes
C---CC---CC---CC---CS
------------------------
As this is done along a whole battalion's line, each company will shrink, and yet keep its dress, maintain the integrity of its front, and keep its men in an effective fighting/maneuvering condition.
Sorry, I didn't intend to write this much this evening, and though drawn out, I hope the details have answered how this procedure works. So in summary...
1. Rear rank men close gaps to the front
2. Files close gaps/dress to the appropriate direction for the battalion's guide/dress point (usually center).
Josh