If you want to customise the JEvents stylesheets or background icons/images without loosing your changes each time you upgrade you can create a stylesheet override. 

Approach 1 (JEvents 3.0.13 onwards)

Create a special CSS file called extra.css and place this file  in templates/{YOUR TEMPLATE}/html/com_jevents/{YOUR JEVENTS LAYOUT}/assets/css/extra.css e.g. templates/beez_20/html/com_jevents/iconic/assets/css/extra.css.

Then override any CSS values you want to change in this file.

Approach 2

This example assumes you are using the ja_purity template and the default JEvents layouts.

Create a folder called templates/ja_purity/html/com_jevents/default/assets and copy the whole contents of components/com_jevents/views/default/assets into this new folder.

Then you can customise the copies css files and JEvents should pick up your customisations in preference to the underlying values in the component folders.

Advanced (pre JEvents 3.0 only)

If you only want to override a few CSS elements then you can get JEvents to load an extra css file.   If you are using a layout other than default (e.g. ext or ruthin)  then create a file in  templates/{YOUR TEMPLATE}/html/com_jevents/helpers/ called defaultinformation16.php (joomla 2.5) or defaultinformation.php (Joomla 3.0).

For Joomla 3.0 this file should contain this content

<?php
defined('_JEXEC') or die('Restricted access');
function DefaultInformation($view){
JEVHelper::componentStylesheet($view,"extra.css");
}

for Joomla 2.5 use this code:

<?php
defined('_JEXEC') or die('Restricted access');
function DefaultInformation16($view){
JEVHelper::componentStylesheet($view,"extra.css");
}

Then place your css file (called extra.css) in templates/{YOUR TEMPLATE}/html/com_jevents/ext/assets/css/extra.css.

Remember to change the references to

"ext"
to match your layout.