First, you won't use the default platform controls because those are instantaneous; instead you'll simulate control as your animations finish.
Basic workflow is like this:
- Character is facing right.
- Player presses left key.
- Test which direction character is facing. In this case it's right, so play the animation to turn from right to left.
- When the animation is finished, and if the player is still holding in the left key, you can then change the character's animation to walking/running/whatever and simulate movement left.
You need to specify animation changes at every key press, but only use those keypresses to control movement when your character is ready. A very controlled, methodical approach is necessary.
For reference, play lots and lots of the original Prince of Persia.