I am trying to find how I can resize a mapped image to view correctly on mobile devices.

We have the website created in Wordpress but this seems to be an obstacle for us.
We have never tried creating a site before so yes we are very new to this.

Any advise would be greatly appreciated.
I know we will be purchasing image mapper but is there something else I need?

an example of the page would be http://cavd.us/products/

I think you'll be best off using media queries for that.

If these were separate links in a list, they could be arranged in columns which could 'collapse' down to one column depending on the screen size.
If you want to keep the image map, maybe try breaking it into smaller image maps they could slide under one another at phone size.
In your theme, you could try the gallery set-up like they have here:

http://wordpress.org/extend/themes/raindrops

Replace the photos with several smaller image maps. Then as they shift to the smaller phone size, they'll arrange themselves in a single column. Go to the link below to see how this typically works:

http://jsbin.com/aseram/1

If you have 5-6 logos per tile, they won't shrink so much as the one large image, so they'll be easier to see/click.