Well watch debates, the people involved often are very good at critical thinking. Try and study and learn their techniques. Also learn about all the logical fallacies, learn how to construct a proper argument. Learn as much as you can about critical thinking. While you are learning try and apply your skills. Argue with others just for the fun of it, and try and respond as quickly and as effectively as you can. You might be slow at first, but you will gain skill with time. Do the same thing in text. Reply to questions people ask, start arguments on forums. Just practice using your skills any way you can. 

Unfortunately though no matter how hard you practice, as mentioned before you will likely find a lot of critical thinking is innate. There was an article on another site, where someone in law school mentioned that some people were just natural born debaters. He said that this sort of skill was something to be desired, and that while he could work to be a good speaker he was never as good as a natural born debater. I think there is a correlation to debating and critical thinking. Some people are just naturally good at analyzing information, and doing so quickly. These are just skills some people are born with. You can improve them, but please don't be discouraged if you can't match the skills of other people. What matters is are you seeing improvement. Are your skills getting better. If after you start trying to improve them, they improve keep at it. You may never match a natural critical thinker, but you can get a lot better at it.