Skyrim Combat Guide: Attacking

Press R, M2 or M1 to draw your weapons. Press R to Sheathe them again. When your weapon is sheathed, you move more quickly then when it is drawn.

If you perform a crime and are attacked by guards, sheathe your weapon to surrender so that the situation doesn't escalate.

To perform a regular attack, tap M1 to attack with your right-hand weapon, or M2 to attack with your left-hand weapon.

To perform a power attack hold M2 or M1. Power attacks do a lot more damage than regular attacks, and have a chance of staggering enemies. Move in different directions (left,right,back,forward) to execute different power attacks.

Many players just hack and slash forgetting about the power attacks. Be sure to  remember to perform power attacks as they do significantly more damage.

The drawback of power attacks is that they cost a lot more stamina. If your stamina is too low, any power attacks you attempt become regular attacks instead.

If you have two weapons equipped, you can't block. However, you can hold M2 and M1 simultaneously for a dual power attack which does extra damage.

Strategies:
Once an opponent is staggered by a power attack, follow up with a quick succession of regular attacks for the kill. Once combat has ended, or if you need to run, always sheathe your weapons so you can run more quickly.