In the interests of clarity, and since it's likely to come up soon, I thought I'd outline the mechanics of fighting in the GCACW series (at least in a large engagement).
Types of attack
There are two types of attacks in the game.
The first is an attack as part of movement, by one token (one division, or brigade if you have a separate brigade). This basically means that you can attack and then move afterwards, or move up to a position and then attack.
This can be done as a "column of march" (where the attack itself costs no movement, but is very unlikely to succeed), or as a hasty attack (1 movement cost), normal (2 movement cost) or prepared (4 movement cost). The more movement cost is spent the more likely the attack is to succeed; the difference between hasty and prepared is going from -1 to +1 to the dice roll for example.
Remember that a Union division being controlled by a commander has between 2 and 7 movement per action, so a prepared attack is a pretty significant chunk of time.
The second is an "assault", and it can
only be conducted by a named corps commander (any of the Union corps commanders, or Jackson and Longstreet) using their own corps. An assault is done instead of movement, and it is the only way to have the men and guns of more than one division fighting at once (they all have to start in a single hex and all attack a single hex), but an assault is also an organizational challenge - it is quite possible that only some of the divisions intended to attack will get the message, and the attack can also fail entirely. (How likely it is to work as planned depends on the corps commander in question - Jackson and Longstreet are both good, but Sigel for example is quite bad. This represents both personal ability and the ability of the corps.)
An assault always counts as prepared.
It is possible to get men from more than one corps, or in more than one hex, to attack the same enemy position. This is called a "grand assault", and
requires the involvement of the army commander (McClellan or Lee). Lee is better at these than McClellan is, again representing both personal ability and the ability of the corps.
The more men are fighting on your side, the higher the expected casualties and the more advantage you have in the dice roll.
Other bonuses
Besides stacking up more men, you can also gain benefits in fighting by the following things.
If you have more artillery, fighting on open ground is preferable.
Defending behind a creek or river gives you a bonus.
Defending in rain gives you a bonus.
Defending completed entrenchments doubles or triples your combat and artillery power.
Threatening the enemy flank and rear by being within two miles (specifically, if you have your own forces adjacent to the hexes which are adjacent to an enemy unit) can give you up to a +4 bonus.
(You need a force of at least 1/4 the strength of the enemy to threaten their flanks - 1,500 cavalry can't present a meaningful threat to 8,000 infantry, but 2,000 cavalry could.)
For flanking in particular, a formation can "refuse flanks". This halves the flank bonus but also gives a +1 bonus to any attackers, in compensation. (This requires movement, but the unit does not leave the hex - it "moves in place".)
The result of fighting
The worst that can happen for an attacker is that they suffer heavy casualties and become disorganized and exhausted (meaning unable to move today, and indeed probably needing to do absolutely nothing tomorrow to recover). An attacker can be repulsed by an attack, but they cannot be forced to retreat from their starting position by failing an attack - remember that the scale is about one mile to a hex.
The best that can happen is that an attacker succeeds for trifling casualties and can then advance into the hex they initially attacked, and if they completely overwhelmed the enemy they may then be able to continue advancing. (This requires winning the dice-off by at least 6.)
If a defender loses badly enough, in addition to casualties, disorganization and exhaustion they can be forced out of the hex they were defending. They can also become demoralized (which means they will be basically incapable of attack for a day or two) by being routed (which pushes them back several miles before they start to rally). A routed division is extremely vulnerable to further attack until it has recovered.
A significant risk for an attacker whose attack has failed is a
counterattack. Defenders can launch counterattacks of their own, and a disorganized and depleted unit is more vulnerable than it would otherwise be.
Note that it is not required for the attacker to advance. This means that units who have entrenched
can make attacks out of their entrenchments - they just need to decide to remain in their positions, since it's only by leaving their positions that their entrenchments are cancelled out.
Examples
Let's have a quick look at an example to illustrate.
In this situation, Jackson is deployed facing off against the whole of the forces of both Williams and Sedgwick, possibly as the result of a bet. He's in a very vulnerable position here, but what are the options for Banks?
Banks could order an attack directly on one of Jackson's brigades with one of his own, and have a good chance of success. He's not threatening the flanks of any of the brigades, but sometimes a brute force attack (such as by the brigade Banks is commanding directly, against Burks - which would have a 4:1 numerical advantage) is the sort of thing that works.
If he rolls high enough to make it a prepared attack (which he'd get on a 3-6 on the dice) he'd be attacking at
+1 from the type
+3 from the strength ratio
but -1 from Burks' artillery being able to be used well on the flat ground.
What Banks could do instead is order Williams to make an assault. This would involve both the brigades Williams is commanding, and if Williams rolls well enough to get them involved he'd be sending in enough troops to give him a 6:1 advantage - and enough artillery superiority to neutralize Burks. This would be
+1 from the type
+5 from the strength ratio
but -1 from the tactical skill difference.
So +5.
This is a better attack.
There are three more options, though.
The third option is for Banks to try and send troops around the flank. Since the Confederate brigades are so weak a cavalry unit could come around the back and outflank (by moving to a hex next to 5402) which would mean that Banks could then have the brigade he's directly commanding attack Burks with a +5 advantage (assuming that Jackson didn't come to his senses and get the hell out of there first). The benefit of this is that Banks could then follow up his advantage by now completely surrounding Fulkerson's brigade and having some of his other forces attack that unit.
As the commander of the Department of the Shenadoah, however, Banks is effectively considered an army commander and can launch a grand assault. The chances of this working properly aren't huge, but if successfully done he could get as much as 14,500 men attacking the 1,000 man brigade of Burks (for a +13 on the dice roll due to strength ratio, plus getting so much artillery into the fight that it'd be the Union getting a +1 from artillery strength, and the +1 bonus from an assault, it'd basically squash Burks flat).
The final option is the crudest one, which is for Banks to order all his brigades to
individually attack Burks. Burks is going to have a relatively good chance of holding off any one attack, but if one of them leaves him having suffered casualties or disorganized then he's easy prey for the next one.