ATaleOfTwoBrothers
This is an easy campaign that is mainly intended to introduce new players to the mechanics of the game.
Rooting Out a Mage
On easy level you should be able to win this first scenario with the troops you get at start, without recruiting. Hang back enough that the undead can't reach you at night, then attack at dawn. Attack the mages with spearmen and the bats with archers; attack the skeletons with footpads; use your horsemen on already-wounded units to finish them off.
On hard, you're probably going to need some reinforcements. It's best to recruit some expendable troops to place in harm's way to protect the loyal troops that you start with--their loyalty will prove helpful later, especially when they level up. You might have an opportunity to send in your horsemen and take out the mage around halfway through, but I'd recommend you spend the extra turns leveling up a couple units to get blade attacks (horsemen to knights or spearmen to swordsmen).
The Chase
The elves are too aggressive for their own good. Keep your units in line- or V-shaped formations with one or both ends anchored on a village; eleven riders will charge in by ones or twos and you should be able to swarm them with foot units.
Again, avoid fighting the undead at the north map edge at night. Let your main body catch up with your cavalry and surround them. When you prevail, make a note of the passwords and take Brena with you. Heavy infantry will be useful in the next scenario.
On hard, a good strategy is to recruit lots of spearmen to wound the elvish riders, and finish them off with your leader or another knight. Ideally, you'll have a paladin by the time you hit the undead in the next scenario. When the enemy wose approaches, you can recall your blade troops or (especially if you don't have enough blade attackers), you can leave the wose behind as you march your troops north. He'll capture a town or two, but you should be able to stay a few steps ahead of him. You can split off a portion of your forces to take out the elvish leader for a few more experience points, just make sure you move enough troops north to take out the undead.
While attacking undead at night is often foolhardy, in this case you only need to take out the dark adept leader, and he's a sucker for blasting units at night. If you march a couple expendable units to the edge of his range, he'll probably oblige, leaving himself open to your retaliation. Even at night cavalry make quick work of a dark adept.
Guarded Castle
One castleful of recruits should be enough to win. Experiment with heavy infantry, they do well against orcs. Resist the temptation to grab the village nearest the castle gate before you've brought your main mass of troops to it; the orcs like attacking any unit isolated there, especially at night. If you put forward a strong battle line on the hills before the gate during the day, you can bluff the orcs into not attacking, leaving you free to march up and take the defensible castle squares and gain a significant advantage.
Once inside the castle, split your troops into two large groups; take one west and the other east. Arne should be in the westward group, as his brother is imprisoned in that direction. But don't miss the chest of gold to the northeast. You'll need to kill the sorcerer before Arne can free his brother. Also note that the scenario is nice enough to give you several more turns after you defeat the sorcerer.
On hard you won't have any heavy infantry to hide behind. The only impact damage available are footpads, and while their high defense can survive a number of attacks, they always seem to get unlucky and die to three or four hits in a row. I guess I'm saying you'll want to bring extra, along with a paladin and a few level 2 troops.
While you're wearing down the defenses at the gate, if you send a footpad or two off to one side inside you can draw most of the skeletons over to that side. This leaves a opening on the other side for your faster units (footpads and cavalry) to break for the sorcerer's chamber.
Return to the Village
There is no need to conserve gold in the last scenario, so recall all of your veterans. Run a small group northeastward over the mountains where two houses cluster; this will distract the orcs while you take most of your forces straight north up the road to the village, circle eastward, and then hit their from the north.
Pick off as many stragglers as you can before the main assault. Goblin riders, which have more movement than the grunts, can often be lured into attacking a forward unit of yours in such a way that your spearmen and cavalry can swarm them.