Joomla 1.0.xx
The colors for the Tooltips on Joomla 1.0.xx are set in the OverLIB JavaScript file.
You will find this file on your Joomla site here:
your_joomla_root/includes/js/overlib_mini.js
Open that file with any text editor.
The file has been "minified" so it is not very easy to read.
Line 21 of overlib_mini.js has the relevant settings. (on Joomla 1.0.15)
This line is one very looooooong line.
I put line breaks in so I could read it more easily
The first 4 settings are the most important.
if(typeof ol_fgcolor=='undefined'

var ol_fgcolor="#F1E8E6";
if(typeof ol_bgcolor=='undefined'

var ol_bgcolor="#000099";
if(typeof ol_textcolor=='undefined'

var ol_textcolor="#000000";
if(typeof ol_capcolor=='undefined'

var ol_capcolor="#FFFFFF";
Caption title background color is ol_bgcolor
Caption title text color is ol_capcolor (white)
Text inside the box is ol_textcolor (black)
Background color inside the box is ol_fgcolor (gray)
Joomla 1.5.x
Tootips are a now core Joomla 1.5 feature and the styles are now in the template CSS file (template.css).
The core template file may be found in your template folder.
Example path:
joomla_root/templates/template_name/css/template.css
Search for the classes below.
/* Tooltips */
.tool-tip {
/*tip container css here*/
}
.tool-title {
/*tip title css here*/
}
.tool-text {
/*tip text css here*/
}