Please would somebody advise me how to arrange for links in sidebars and center of website to change color when curser hovers. Settings in ATO do not work for me.

What version? what is the url? what EXACTLY have you tried, be detailed.

Version 3.7.1. on www.arttoursltd.co.uk

I have tried editing the "body, text & links" section of the Atahualpa overall "style & config menu"

I have added various codes into add HTML/css inserts e.g.

a:link {
color: #12448;
}

and

div.post a:link {
color: #12448;
}

Your help is appreciated

did you look at the themes widget options?

Yes, I have edited the widget list items section.

I tried the following code which produced an underline that changed colour but I could not remove the underline and get the link itself to change colour

a {
border-bottom:1px solid #cccccc;
padding-bottom: 2px;
}
a:visited {
color: #09C;
text-decoration: none;
}
a:hover {
color: #333333;
border-bottom:3px solid #AD3417;
padding-bottom: 2px;
text-decoration: none;
}
a:active {
color: #006;
text-decoration: none;
}
a:link {
text-decoration: none;

The settings for the links n the widget area will be more specific than the css you specified in the previous post. You should learn how to use FireBug in FireFox to examine the emements and determine the CSS that is being applied

Atahualpa provides settings for links in a list, but because most widgets are provided by other authors, there is no way to know what the exact CSS for a particular widget link might be.

Why here:
Overall Style & Config - Body, Text&Links I can't see and change these parameters:
Link Default Color and Link Hover Color. I mean I can but I can't see and choose color just here. Now I can make it by changing digits without showing colors.
I speak about 371 version.
In previous versions was more convenient interface.

Nothing changed, try disabling your plugingps to see if there is a conflict

What is this plugingps? Where is it I can see?

It's a typo - plugin's