To obtain a score, you must finish the puzzle at least once with a number of moves below the limit (for more information, you can read the article How many moves do I have to complete the puzzles?). The score is made of two things: the time you took to complete the puzzle, and a number of stars (from 1 to 3) which shows if your performance was good or brilliant.
You can see your score at the end of a puzzle or on the map. When you play, your score automatically shows if you complete the puzzle within the time limit or if you reach the maximum number of moves. On the map, the puzzles you have already completed have stars above them. Click on the number of a puzzle to check your score. The score displayed is your best score on this puzzle.