It's really easy. Once you take your class (which can be done a ton of places for widely varying prices) just call your county sheriff's office or a neighboring county and tell them you need to come in for ccw stuff. I did it in Deleware county, and they were super easy and cooperative. Just fingerprint, get a pic snapped, wait a week or two and pick up your license.
CCW on a bike is a godsend, because before I had to open carry to transport a firearm on my motorcycle, and you definitely get some suspicious looks. I remember Utah CCW being really easy, and covering some more ground as well, but I may be confused.