When you are looking to make a text-to-text connection, it helps to think of other stories, books or poems that you have read that remind you in some way of this book. That way you can say that the two pieces are similar in some way. Take for example a story by Ray Bradbury, called "There Will Come Soft Rains," which is another tale of a society that is wiped out by war. It shows the impact on a small family. I provided a link below if you want to read it. You just tie the two stories together, and how they are similar.
When making a text-to-self connection, you have to ask yourself how you relate to any of the characters or situations that are presented or discussed in the book. Do you relate to some of John's insecurity, or his relationship with his father, or his fear in the face of unknown circumstances? Do you recognize any of the remnants that he comes across as he reaches civilization? Have you ever had a secret or a super huge burden to carry that you didn't know what to do with? These are all ways that you can make personal connections to the text.
For text-to-world connections, think of what this story is saying about our world, or how they are similar or tie together. As John reaches civilization's remnants, what does he notice about them? Why do you think they were wiped out? What mistakes does John not want to make that we are making in our world today? For example, look at the end where John's father states, "it is better the truth should come little by little," which means that they should build civilization slowly, thoughtfully, and carefully.
I hope that these thoughts help; good luck!
I made connections with little hints like the rats and the washing areas that said hot but it wasn't hot. Those things gave me reasons to beleive that John was in New York City.