For rifle training there is an Appleseed shoot coming up. It will be April 19th in Nephi.
Rangemasters in the Provo/Orem area and several other gun shops offer CCW training. Even if you decide not to carry it offers a good start on basic pistol handling skills.
I did a brief Google search and found http://utahfirearmstraining.com
First I've heard of them, so I can't really comment. Might be worth checking out.