Thought process in a chess game is vastly different among novice, average, expert and grandmasters. It's a gradual learning which comes with time, experience and passion.
The novice players see moves to immediately gain a piece, give check, exchange a piece, etc. They generally don't think one move ahead.
Average players have acquired some tactics, strategic play, knowledge of positional advantage and make their moves according to these combinations. They scan the board hard to find a better move than the move they have decided to be the best.
Expert players develop intuitive knowledge about other players style of play. They are well verse with chess openings and can take advantage of other player's opening blunder. They are good in strategic play and see the board ahead after 3 to 5 moves combination. They normally play for checkmate rather than immediate positional advantage, or short term gains.
Chess grandmasters have excellent memory, and they can recall games similar to the position shown on the board. They don't think much, as their mind automatically thinks only about the best moves as it comes with experience. They are very good in analyzing variations in a chess position. They always tend to make moves that result in deterministic checkmate rather than non-deterministic positional play, although the later can be converted to former.