How Do I change existing theme to a new one without losing content?
Technically you won't loose any of your content since Drupal's theme layer is seperate from the content. Depending on how your previous theme is set up (templates, theme functions, etc) it can however happen, that the display of some of your content might not work / work differently in another theme. 

A good starting point for learning more about Drupal's theme layer is the Theming Guide which is part of the Community Documentation at drupal.org. A more advanced view on theming can be found in the chapter 'Themes' of the book Drupal 7 – the Essentials which you can actually read online at drupal.org.