you can do so: take into two variables your character's x,y coords*cell_width, where x and y are the cell indexes (from 0 to 63, or from 1 to 64); when you want to move your character into another cell, you need to calculate the new coords. At that moment, you know the start and finish coordinates of the character movement and with a simple function you can move it at which speed you prefer.
I hope I have been helpful :)
I hope I have been helpful :)