Thinking, Fast and Slow is full of illustrative experiments and examples that you can even try on yourself!
System 1 produces instantaneous responses to environmental stimuli in the form of cognitive, emotional and physical responses. For example, seeing the words "banana vomit" immediately causes frowns, an aversion to bananas, and recognition of other objects, concepts and images associated with those words (e.g. the colour yellow, nausea, words associated with bananas etc.). This response is automatic; you did not will it, nor can you stop it.
As such, System 1 can be primed. If you have recently heard the word "eat", you are temporarily more likely to complete the fragment "SO_P" as SOUP, whereas if you had just heard "wash", you are more likely to complete the fragment as SOAP. Priming is not just verbal: you also find things funnier if your face was contorted into a smile position while experiencing them. Furthermore, if you are asked to nod while hearing a statement, you are more likely to accept its conclusions!
The effects of priming reveal just how susceptible we are to being influenced without our knowledge. For example, voters asked to pass legislation requesting more funding for education were more likely to vote for such legislation when the polling station was at a school!
When you are at ease or in a good mood, you are more likely not to invoke System 2 to analyze situations. As such, you are more likely to accept the intuition of System 1. A lazy System 2, therefore, results in your accepting of ideas and concepts that may not be true.
Frequent exposure to words and ideas also results in your making positive emotional association with those words and ideas. This occurs even when such words are presented quickly (e.g. subliminally). In this case, System 2 is unaware, but System 1 is responding to the environment and causing you to permanently think a certain way!