A player cannot enter the blood pool if his movement would finish on a space that is already occupied by another player.

In the illustrated example this would be the case (like mentioned in the text) if the player would (beginning at the start position of the token!) move 2 steps up and then move 3 steps to the left: the token would enter the pool with its last step.

He could do so, if the space on the other side would not be occupied by another player but as you can see in the example, there is already another token. He could also enter the pool if he had more than 1 step left.

The movement shown by the arrow is OK because the movement does not end on an occupied space.

The way a token slides is always the way of his entry direction, but if he stops on the blood because of a stone (like in the example after step 4) you can then decide in which direction to continue sliding if more than one direction is possible. You could even stop there if you decide not to use the remaining steps.