Casualties are removed in exactly the same way as missile casualties. You may wish to re-read the Shooting section at this point. Remember that both sides fight in hand-to-hand combat, so models removed before they have a chance to strike cannot fight back. You will find it easiest and most practical to remove casualties from the rear ranks of units rather than from the front. Although it is the front rankers who are actually fighting, rear rankers would quickly step in to fill any gaps in the line, so it is preferable to remove these straight away. However, the rear rankers who step in to the front line cannot fight that turn - all they can do is step into the gap.
To remind you how many casualties have been suffered do not take the casualties off the table immediately, but place them behind the unit. There are two reasons for this which will become very clear as you play. Firstly, if you remove models from the back rank rather than the front you will have to bear in mind that some of the front rankers are actually rear ranker who cannot fight. Leaving casualties on the table will remind you how many casualties have been suffered and so how many models are left to fight.
Secondly, you need to know how many casualties have been suffered when it comes to working out which side has won the combat, and having all the casualties in place behind their units helps to make this clear.
Some models have several attacks, not just one. It is possible that a big creature, such as an Ogre or Minotaur, or a huge monster, like a Dragon, succeeds in inflicting, say, 3 or 4 wounds even though the model is only touching 1 or at most 2 enemy models. When this happens the number of casualties is still the full number of wounds caused, not just those models directly touching the attacker.
This is because combat is not the strictly organised linear affair that it appears. When the big creature attacks it slashes in one direction and then the next, stepping forward and aside to strike new victims as its enemies fall beneath its feet. This means that a monster or a powerful hero may be able to destroy many more enemies than he is touching.