Combat Tactics 1

To battle!

Early in the game, get your Daimyo out of the castle and have him lead an army. The honor bonus an effective general confers to his troops is invaluable; it will the turn the tide of many of the early battles. However, you'll also want to cultivate at least one more general so you have greater flexibility later in the game. Create a secondary army and use it in the easier early battles to train its general to a higher rank. 

When you're facing a tough battle with defenders holding a river or a stubborn hilltop position, you're often better off throwing overwhelming numbers at him and using the "Resolve Combat Automatically" option. 
This generates the outcome through a formula that puts more weight on numerical superiority than tactical advantage. This is also a good way to use hordes of Yari Ashigaru; throw them at a province and wear it down using the automatic combat resolution. Cheap, yes but so effective.

This automatic resolution is also a good way to get around the 16-unit limit on the tactical battles. Alternatively, you can attack a province with more than 16 units, but they'll fight in the order in which you drag them onto the province. 
The first 16 will show up to fight and replacements will arrive whenever your total number of units drops below 16. 
You can send tired or depleted units off the map to make way for reinforcements with the withdraw (CTRL+w) command. 

You should also withdraw any valuable high honor units that start to get clobbered too heavily. Minimize the casualties among your high honor units by using them properly.
When you replenish depleted units, you're watering their honor down with the replacements, so it's important to keep as many of your veterans alive as you can. 
An effective army will include a fair number of disposable troops, particularly when you're expecting a lot of casualties. 
This is where the Yari Ashigaru earn their keep. Ashigaru are just hastily mustered peasants; sometimes they'll turn tail and run when faced with high honor troops or Warrior Monks. 
Use them as garrisons or a way to pad defenses to discourage attackers, but don't count on them as the basis for an active army. Instead, your default grunts should be Yari Samurai and Warrior Monks.

Strengths and weaknesses

You will lose your cavalry if you expect them to fight well on their own. 
They are good for speed more than anything else. Although Heavy Cavalry are clearly the best units in the game, the Yari and Archery Cavalry are mainly useful for their mobility, giving you the flexibility to adapt to the situation or strike when you see an opening. 
For instance, when you can catch a unit in the process of changing formation or position, a quick charge can be effective. 
It's fair game to rush an enemy's general with your cavalry, as a dead or fleeing general has a dramatic effect on the way the rest of that side's units will fight. Keep all cavalry out of the forests. 
Archery Cavalry are great as a sort of hit-and-fade mobile artillery that can attack from a distance and pull back before anyone can reach them to retaliate. Use them to thin the ranks of heavy hitting troops like No-Dachi.

No-Dachi won't hold up under attacks, so use them almost exclusively for quick offensive pushes. Conversely, Naginata are the best defenders, so use them to hold off attackers. 
Archers are good against Warrior Monks if you don't have your own monks to attack them.

Arquebusiers and Musketeers are much cheaper than Archers, but they're not nearly as flexible or powerful. Whereas the Archers have real reach and can pack a punch if the wind isn't too strong, guns are only effective at relatively close range; they're better used to thin out oncoming melee troops. 
Since they have a slow rate of fire, arrange them in ranks three men deep to maximize their firing rate. 
Archers, however, should be arranged in ranks two deep for maximum coverage. Put missile units into loose formation if it doesn't spread your unit frontage so broadly that some of your men can't reach the enemy; this will minimize their casualties from return fire. 
Note that you can suffer from friendly fire if you give specific orders to attack enemy units engaged in melee with some of your men; otherwise missile attackers won't voluntarily risk friendly fire casualties.

When deciding when to attack, don't always assume that you should wait for a fine day in spring. 
Rainy or windy days are good for going up against an army heavy with Archers whose effectiveness will be minimized. 
It's okay to attack through bad weather if you can afford for your troops to be tired from marching across the map if you outnumber your opponent, have a higher honor, or have a lot of light troops that don't wear heavy armor, you can afford the long march across the map through snow or mud.

River provinces are ridiculously easy to defend, so regard these as crucial chokepoints on the strategic map. 
To take advantage of a hill, which will be the deciding factor in many battles, don’t sit on the very top. This is risky, because if you're driven a little ways backwards, suddenly the enemy has the height advantage. 
Talk of hills is a little deceptive, since it's really the angle of the slope that matters. If the enemy has staked out a slope, try to maneuver to his flanks to minimize his advantage. This is especially easy to do if you outnumber him and can approach him from two sides. 
When defending, choose a hill at the back of the map so the enemy has to wear his men out by walking a long way; this is particularly effective in bad weather.

Making the best of it

The first opponent you have to conquer in battle is the interface. 
Pause the battle often to assess your situation and give orders. 
Until you've made physical contact with the enemy, use your army as a single unit. Select them all (CTRL+a) and use one of the formations, generally 'skirmish center', to approach or await the enemy army. 
Larger armies can be divided into a couple of chunks using the unit grouping controls. Generally, you should let the formations arrange your individual units, who tend to function pretty well without being manually given orders. 
One exception to this: when a unit is closing to melee, select it and give the target a quick double-click to order a last minute charge.

When an enemy army is trying to outflank you, there's an undocumented command to rotate your formation: hold down the alt key and press the right mouse button. The selected units will rotate to face the location of the cursor as you move it around and a ghosted image will show you their target facing.
Let off the right mouse button when you have the facing correct. 
If you've selected a spread-out line consisting of multiple units, hold the cursor at a distance from the units to keep them from curving in a semi-circle around the cursor's location.

When you double click a unit across the map, you can bypass the slow moving camera by tapping any camera movement key to instantly jump to that unit.
The kill ratio bar located over the minimap measures the absolute number of men on each side who have been killed; the longer the bar, the more men have been killed. When the bars meet in the middle, they readjust to represent relative numbers.

To win a battle when you're the attacker, you have to either run all the defending units off the map or put them in a state of rout. If you just let them fall back and reform, you'll lose the battle.
Make sure to check the forests for hiding units. 
Battles in fog can be really hard to win for this reason.