Well, Google will turn up a lot of search results with articles on improving your critical thinking skills. Here’s a quick (for me to write up) exercise off the top of my head:

Read the headline of a news article and try to guess what the content will be. Then, read it line by line, asking yourself if each statement is fact or opinion. If it’s fact, ask yourself how the fact could be verified, and verify it if necessary. If it’s opinion, ask yourself why the writer might have such an opinion, and if it’s reasonable. Also, watch out for the passive voice — sentences where the doer of the action (“agent”) is not mentioned. Ask yourself who the agent is (if one even exists…), and why the writer has chosen not to mention the agent explicitly. Keep reading, line by line, clause by clause. You might be shocked at how much garbage passes for journalism. This exercise should provide hours of education and fun.

Lynne, it’s perfectly correct grammar — it’s simply not a question or even a sentence. 

“How to Train Our Critical Thinking Skill” is a phrase that functions as a noun, so it can be used as a title, or as part of a full sentence: “We’d like to know how to train our critical thinking skills.”

As far as your question, I'm fairly sure that Jerry is an expert on this topic, so I’m hoping he has time to provide a real answer :)