How Do I change existing theme to a new one without losing content? Can someone lead me to documentation that explains how I can change an existing Drupal theme to a new one without losing all of my existing content?

The blog I manage is currently set up on the Omega 7.x 3.1 framework, with a semi-custom subtheme. We would like to install a new theme with more out of the box capabilities and a better design but it is important that the two years of published articles are maintained in the current chronological order and with their image content, etc. 

Any help finding the instructions on how to accomplish this will be a great help.

Best wishes from Spain!
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.