So what's new? First of all, weapons only have one damage rating. Gone are the three attack types from Morrowind - Chop, Slash, and Thrust. Instead, the damage rating simply indicates the base damage the weapon can do. That damage value will be modified based on the attacker's skill, luck, fatigue, type of attack selected (more on that in a second), and on the target's defensive stats, armor, fatigue, and whether or not they're blocking and even the weapon's condition comes into play.
In Morrowind, you selected the type of attack you wanted to do (Thrust, Chop, Slash) by pressing the attack button in conjunction with a movement key. Or you just turned on the "Always Use Best Attack" option, since for some weapons there wasn't much point in choosing anything BUT the best attack. For Oblivion, selecting attacks is different.
To perform "normal" attacks, you just click the attack button to swing your melee weapon. If you click again at a certain point in the swing, you can perform another attack on the back swing - so you can do multiple slashes with your weapon by properly timed clicks of the attack button. Each time you attack, some fatigue is burned.
We've also added a new kind of attack called a "Power Attack". Power attacks do significantly more damage than normal attacks, but they take longer to perform (leaving you vulnerable) and burn more fatigue. You perform a power attack by holding the attack button down briefly while either standing still or selecting a direction. For example, if you hold down the left movement key and press and hold the attack button with a sword equipped your character will do a cool spinning attack while moving to the left. (No, the camera doesn't spin in first person - trust me, you'd need a bucket next to your gaming setup if we put THAT in!) And as your skills progress, you earn new power attacks.