Look to see if any of the rifle clubs have a public day. If they do, ask if an RO (range officer) will work with you. Go to the NRA website and see if there are any NRA rifle courses in your area (look for the NRA Basic Rifle). I would also suggest getting a rifle in .22 Long Rifle (get the same action as your .270 WSM - bolt, single-shot, etc.). A .22LR can pay for itself quickly in ammo cost savings. Once you have taken a rifle safety course, take the hunters safety course.
I recommend caution if you use a Leadsled or any device that is solid against the butt of the rifle. Some have cracked their stocks using these type of rests.