Here's the formations and some explanation based on 180+ days on campaign in this very entertaining mod:
Shield Wall: Infantry formation no greater than 3 rows deep. It seems that no matter how many troops I have they never form more than 3 rows of men. I've tried this with as few as 20 infantry and as many as 350, and it's always 3 rows deep. Also, they will form up on your left side. If you imagine the shield wall as a rectangle with the long side facing the enemy, your character will be at the top-right corner of the rectangle if you tell them to form a shield wall without pointing to a specific location. This formation is the most common and frankly the most useful, you can win against numerically superior forces if you use this on a hill and tell your men to hold while making use of your battle cries (u and b keys).
Ranks: This seems to form your troops up into a single-file line that attempts to face parallel to the enemy. Useful for archers or cavalry prior to the charge. I've noticed a bug during sieges where if you are attacking and order your archers to form ranks outside the walls, they will line up single file perpendicular to the wall, and generally only accomplish dying with any talent. I can't seem to get them to line up properly for the life of me during a siege, but that's for another thread.
Square: Exactly what it implies. A big square of dudes all facing the same direction. Can be handy to order this during a melee if you're getting roughed up, as it allows you to retreat into the center and be protected by your men. Other than that, it is generally tactically inferior to the shield wall or ranks formations
Wedge: Well, it's a wedge. Yeah, like cheese. Historically used by cavalry to "crack" and panic infantry formations. In-game it doesn't seem to work all that efficiently compared to other formations. Being able to order your cavalry to form a shield wall (lol) and then charging them works just as well, and frankly if you're using your cavalry right (as in, charging them into the rear/flank of enemy infantry) the formation you use doesn't really matter as the enemy will usually panic and start to route anyway.
As for tactics, it's really pretty simple. Find a hill, form a shield wall, and stay close to your men. One thing to note is that if you move too far away from your men they seem to decide to run off to the corner of the map. They don't route, they just jam up against the invisible wall and stand there. It's super annoying and can really ruin your tactical genius. If you stick close to your soldiers they usually stay where you order them, though if you are really outnumbered they will sometimes run off.
Also, archers almost never stay put. I quit using them altogether because it's super frustrating having a specific group of soldiers run off every time you turn around. If you tell them to follow you and then stand in one spot, they seem to stay put. They're like freaking toddlers, the second you look away they're halfway across the battlefield picking flowers completely oblivious.
The running away problem affects all troops, so your days of ordering your men to hold in a big fancy formation while you ride off to merrily lance away are over. If you do this in this mod, you can expect all your soldiers to be in a big pile jammed up against the farthest and most inconvenient invisible wall of the battlefield in complete disarray. Is it annoying? Yes. Is it somewhat realistic? Sure, probably. I can't imagine the men being motivated to stand around while their commander rides off over yonder hill for whatever reason.
So, to sum it up. Stay close to your men.
Also, most of the pole arms in this game do not allow you to "couch". In fact, there seems to be only one pole arm (the Koplon) in the entire mod that allows this "couching" and I have yet to ever see it for sale, anywhere, ever. So forget that couched lance thing.
Bows don't get awesome until you get to around 250 skill points. Right now I'm rocking a power draw of 10 and 301 skill in bows, using a masterwork longbow, and the aiming reticule stays small even zoomed in, and I consider it my primary weapon. If you want an archer character, you have to basically max out your skills to be worth anything, and it wont pay off until you're around level 30. Crossbows are extremely rare and can only be found in the north as the pictish crossbow. It's damage is ok but the long reload time makes it not worth keeping, especially considering the damage output you can get out of bows with a decent power draw skill.
In sieges battlecries are your best friend. Rush up the latter and hit b to drive the enemy back and allow your men up onto the walls proper, then sprinkle in a little "u" here and there and you should be fine. Gesgiths (from the Picts) are amazing tier for a siege.
On companions: Do what you like, so far I have 4 with me and I've given them all heavy war axes and thick mail, and they are worth 50 men each. Seriously. I find that when I give them swoard/shield they spend more time blocking than swinging, but when I give them a big 2 handed axe they just hack their way through 20 guys before finally going down. Note that your companions will get knocked out in almost every battle anyway, so I prefer that they take as many with them as possible.
Clerics/priests of woden: these dudes are great, keep one or two in your party and you can talk with them to raise morale. Very, very handy on long campaigns. In combat they are useless however, so keep them at the rear and safe as much as you can.
Hope the wall of text isn't too much, and thanks again for the work that went into this mod, it's been great fun.