You develop thinking skills by practicing thinking. Find a new hobby, or a type of puzzle you like to do. Take on a home improvement project, or learn a new language. Any time you exercise your brain, you are learning new thinking skills. Of course, being in school helps develop thinking skills all the time!
I assume you are talking about the ability to problem solve, or mental gymnastics. I have found that my students' abilities to examine a situation and to analyze its complexities have increased since I began incorporating the use of analogies in my lessons. Throughout the year, I have slowly moved from the most obvious synonyms and antonym based analogies, to ones that require deep and thoughtful consideration. I have gradually withdrawn the level of support available to them, but they have been able to rise to each challenge.
Plexars are also a fun way to challenge the brain. Amazon.com has several books that you can purchase. A Plexar or Quizlet, as some sources call them, are visual puzzles that rely on the physical location of a word within the puzzle to transmit its meaning.
represents the expression "Buckle up".