Okay let me explain the mechanic... Its very simple... The goal is to reach the green square. There are two ways you can move the pawn... 1. Select the arrow and use it by clicking the grid slot. 2. Use a card.. select card, fill the slots using the arrows and activate. Then the pawn will move in the left to right order of the card slots and if all the movements were successful you gain power of that card piece and you can move one time like that piece. And for the piece movement just click on a square where you can move according to that piece.
......... And keep in mind you have limited use of arrows and cards in each level that you can see in the top right corner. Hope this helps.
Here is the solution of the first puzzle so that you can understand the mechanic.... 1. Use up arrow to move up one square... Then use rook card and fill the slot with right arrow and activate... Then pawn will move right and you gain the rook power... So now you can move like a rook so just click on the green square and you will get there.