Knowledge (combat and tactics) covers all aspects of battle - arms and armor, fighting styles, siege warfare, and large- and small-unit combat.
Arms and Armor
On a DC 10 check, the PC can determine, with a round of examination, the overall quality of a given weapon or piece of armor– normal or mastercraft, and whether or not the item has any damage that would reduce its effectiveness. He can also tell an item's mastercraft level with a check vs. DC 10 + mastercraft level. On a DC 20 check, he can tell if it is magical, though not what enhancement bonus it has or what it does.
The PC can determine the material of a given weapon or piece/suit of armor as a full-round action. In most cases, like iron, bronze, or steel, a check is not even necessary – this is for more exotic materials like dragonhide, adamantine, or elven steel. The DC increases by the relative rarity of the material (the DC is 5 + the Craft DC modifier).
On a DC 10+ check, the PC can determine who made a given weapon or piece/suit of armor, and when. The base DC of 10 is for still-living smiths, legendary smiths whose work is well-known, or smiths whose marks are fairly well-known. The DC increases for modern smiths who are less well-known (a smith in a small town), who lived long ago and/or are rather obscure and/or who have very few examples of their work left.
Fighting Styles
The PC has studied (and probably trained in) various fighting styles, and can identify them.
On a DC 15 check, the PC can determine someone else's fighting ability (level) in relation to his own – much worse, about the same, better, much better, etc. The PC must observe the other person training or in battle to make an accurate analysis; merely observing someone and making a judgment based solely on his gear and the way he acts and carries himself is a DC 25 check.
On a DC 15+ check, the PC can determine someone else's fighting style, and can apply this knowledge to counter it. He must observe the other person fight (himself or someone else) for at least three rounds, or train (go through forms or spar against imaginary opponents) for five rounds; if the check is successful, he gains a +2 bonus to attack rolls and Armor Class when fighting that particular opponent. This bonus lasts for one day per level the PC has in a martial class (see below), or until the other person gains a level, whichever comes first. The modifier for this check is + or -1 per point of difference in their base attack bonuses; if the other person's level is lower, the DC is reduced, and if higher, it's increased.
Large-Unit Combat
The PC has studied large-scale combat (battalions and armies) and knows how such groups act and react, to the point where he could lead such a group in combat.
The check is the same as small-unit combat, except that the DC is 15, and bonuses apply only if the number of those involved on the PC's side is 21 or more. The DC increases by +1 per 50 people under the PC's command – there is no upper limit here. The PC must have a relatively clear idea of the battlefield and of the forces involved; making a plan without knowledge of the area and/or of the enemy increases the DC by +8 for each.
Small-Unit Combat
The PC has studied small unit (squad-level) tactics, and knows how such groups act and react, to the point where he could lead such a group in combat.
On a DC 12 check, a PC can set up a plan of attack that can grant a small unit (up to 20 people) a +2 competence bonus on attack rolls and saves for the next combat. Alternately, he can give commands during the first round of combat that also grant this bonus. The DM can increase this for a particularly good roll or plan. The PC must have some idea of the layout of the area and/or the enemy they are about to face in order to make a plan, or must be able to communicate with his comrades during the battle. If the battle changes significantly (the enemy receives reinforcements), the PC must make a new roll to account for the changes. If the check fails, he and his comrades lose the bonus.
The DC increases by +1 per 2 people on the PC's side involved over 6, up to 20 total – so 8 PCs would be DC 14, 10 would be DC 16, etc. Making a plan without knowledge of the area or of the enemy increases the DC by +4 for each. Being unable to communicate with comrades during the battle prevents the PC from making a check.
Siege Warfare
The PC can apply his technical know-how to using siege engines (as opposed to building them, which falls under Knowledge (architecture and engineering). In order to use this skill, he simply makes a DC 10 Knowledge check; every 5 points over the DC grants a +1 bonus to the attack roll for the crew when using that siege engine. This bonus can be applied to one engine at a time, and works only if the engine is firing at the same spot - if it moves or changes targets, the PC must make a new check. He can also make a new check at any time if he wishes to try to improve the bonus - this reflects knowledge gained from observing how well previous shots worked.