Here's an example of grid-based movement with C2's tilemap object. Using a tilemap layer for collision checks makes it really easy to work with the grid. C2 gives you the ability to check and change a tile at certain coordinates. This can be used to create a level editor, but also to work with grid-based movement.
You'll find detailed comments in the capx file to guide you through the code. It shows how to have a character that moves fluidly on the board, with collison data handled and updated on a Tilemap object.
And if you're interested, this video explains grid-based movement/collisions from a game design standpoint: