Changing colors of drupal tables
There are a couple of ways to do it. Here are two of them:

 Through your theme  


write your own mainstyle.css file.
place it in your active theme directory (directly or in a folder that you create there) 
go to that theme directory and open the file: [themename].info (e.g. bartik.info or myAwesomeTheme.info) 
add stylesheets[all][] = mainstyle.css after the existing stylesheets. (or stylesheets[all][] = css/mainstyle.css if your stylesheet is placed in a folder called 'css').
flush your cache


This way drupal will include your stylesheet.

 A simpler way to do it , with the help of a module, so that you don't touch any of your files, is


download the module  css injector 
enable the module
go to configuration -> development -> css injector (admin/config/development/css-injector) 
create a new rule and give a name to the rule: e.g. table styling 
Finally in this rule write your CSS  e.g. td {background-color: red;} etc 


Tip: If you want to target your elements (e.g. tables) correctly, then you may need firebug, which is an extension for Firefox.