I'm assuming you have a variable determining the enemy direction. Also, assuming you're just using the four cardinal directions.
You can just do a simple comparison of the enemies x,y coordinates compared to the player's.
sudo code:
if enemy x > player x // player is to the left of the enemy
enemy face left
else if enemy x < player x // player is to the right of the enemy
enemy face right
else if enemy y > player y // player is below the enemy
enemy face down
else
enemy face up
This will make your enemies almost always face left/right. You can get more involved once you get this working by comparing the deltas of the enemy x/y compared to the player x/y.
Something like:
delta x = abs(player x - enemy x)
delta y = abs(player y - enemy y)
if delta x > delta y // Enemy is further away on the x axis than the y axis
make a choice of facing left/right
else
make a choice of facing up/down
Hope this helps you get started.