Yes, a regular guy can take the class.
You take the Utah specific class and it also satisifies the requirements of the other states, complete the class turn in your paperwork and get your permit.
You may or may not need to have a carry permit in your home state, that is have to look into. I'll be taking the Utah course in Feb and will find out more then.
Regarding purchases, you can purchase a gun in any state regardless of carry permit, but you can not take possesion of the gun and it will have to be sent to a dealer in your state of residence where you will fill out the required paperwork etc.
Also remember that when carrying in another state, you are subject to their laws and conditions.