This is how I was taught, and teach. ;D
Attacking is easy. Say we have two units: Hans the swordsman, and Waagh the goblin archer. Hans is attacking Waagh. He rolls the D6, comparing their respective WS (Weapon Skill) abilities, and consults the chart. He rolls a 5, which hits. Then he has to compare his S (Strength) versus Waagh's T (Toughness) to see if his hit has sufficient force. He rolls a 4. Waagh is hit with sufficient force, but now Hans must type the hit. He rolls...a 1. Waagh is not removed from combat, but simply knocked down. He will get back on his feet in his next turn.
Waagh's plight has not gone unnoticed by his orc pal, Blarg. Blarg charges Hans. He has an M of 4, and as he's chargina, he has to take the most direct route toward Hans, traveling up to double his speed and then making his attack. He calculates his charge route and is barely outside of the Intercept range of Heinrich, one of Hans' friends. Charging units always roll to attack first (Unless the charged unit has a spear.), so Blarg rolls. He compares WS and Hans' WS, and rolls a 4. This is a hit. However, as Hans is armed with a sword, he may roll a parry. He rolls a 6. Blarg's hit is parried. Now he gets to attack back. He rolls a 5, hitting Blarg. He rolls to wound, and rolls another 5. Blarg has an axe, so he doesn't get a parry roll. However, he has a shield and light armor, so he gets to roll an armor save. His shield gives him an armor save of 6, and his light armor gives him a save of 6, so his armor save is 5. He rolls...a 1. The hit goes through. Hans types the hit. He rolls a 6. Blarg is taken out of action.
On Waagh's turn, he gets up. Though he is an archer, everyone gets a free dagger in Mordheim, as such things are easy to come by. He wants to attack Hans, but he just got up, so Hans gets to attack first. Hans Rolls his attack...a 1. Waagh is safe. Waagh rolls his attack, and gets a 4. Barely enough to hit. He rolls to wound and gets a 6! This is a critical hit! He rolls on the special Critical Hit table to type the hit, and rolls a 5! Hans is Sliced, automatically takes 2 wounds, and Waagh gets +2 to his injury roll to type the wounds. He rolls a 3, adds his 2, and gets a total of 5. Hans is out of combat!
After combat, Blarg and Hans both have to roll on the table, to see if they recover. Hans rolls a 2, meaning he's slain by Waagh's attack. He's scratched out of his warband's roster. Blarg was a hero though, so he rolls 2D6, one of them marked as a 10's dice, the other as a 1's dice. He rolls a 17. Bad luck, but he's not quite dead! He has to roll twice more on the injury table. He rolls a 24. Madness! He then has to roll on the Madness table, and rolls a 3. He now suffers from Stupidity. His other roll on the injury table is a 36. While he was lying there, his possessions were stolen. Now he's unarmed, unarmored, and stupid in the city of Mordheim. Truly a desperate situation.
Waagh gets 1 experience for not being put out of action during the battle. Were he a hero, he would've gotten one more experience for downing Hans. However, he still gets to Advance, as he gained JUST enough experience. He rolls 2D6 on the chart and gets a 10! This means that he's no longer a Henchmen, and becomes a Hero. However, as he is a goblin, the orcs in his party don't take too kindly to an uppity little goblin telling them what to do, and Waagh is subsequently executed by his own people. Blarg is returned to his camp, but being stupid and an orc, no one really notices.