Hey welcome from South Central Kansas!!
I just took my CCH class this last December. Most of the Kansas replies are correct, but I'll try to add a few details.
First thing, you set up/enroll in a class to take. I had the choice of a couple of 4 hour evenings after work or an 8 hour class on a Sunday. I decided to use a full Sunday and have it done. It went fast, the guy was funny and we all had a good time. Even though there is a multiple choice test at the end, the big requirement is to be lectured for 8 hours. The test we did, we also self checked as the instructor went over each question with the class. He didn't even look at them before giving us our letter of completion.
I took mine at an indoor range and therefore was able to take the shooting portion of the test at the same time. As others said you can use whatever gun you choose, pistol/revolver any caliber. The shooting requirements are 25 shots. The first 5 are from 3 yards and are one handed, the next 10 are from 7 yards and are two handed and the last 10 shots are also 2 handed at 10 yards. Out of those 25 shots you are allowed to have 8 outside of the silhouette and still pass. It seems the guys will continue to work with you if you have problems, I think a big part is to see you operate the weapon safely and that you can reload etc.
But in this area you can find classes at 90 bucks or less pretty easy. I wouldn't think it would be too different up NE. Other than the class, it's all money and time. I believe it's $132.50 to finish up the process. But get the CCH application and fill it out. Attach one of your photos (that you have to pay for before hand from your big corner drug store, 10.00 bucks..?) and a copy of your CCH certification. The Sheriff's Office keeps 32.50 of it and takes your finger prints, and sends 100 to the state along with your application etc, it takes two seperate checks.
After that process it's all a waiting game, I believe mine took 65 days to get back to me from the state. You will recieve a letter of acceptance which you take down to the driver's license office and they will take another 15 bucks, I think it is, and take your picture and give you a temporary "receipt" type license to use until you receive your real license in the mail within 2 weeks. Your license will look exactly like your driver's license other than saying Concealed Carry permit.
I hope this helps you understand the process.