They have a limited number of rifle and muzzle loader tags (I believe 15,000 of each), and unlimited Archery tags. Its $65 for your hunting license and $393 for a general elk tag. Extremely cheap compared to other states for non-residents. Like stated above, if your looking for a trophy class bull then you might not want to waste your time and money on the OTC tag. But if your looking for a fun hunt with your dad where size doesn't matter, then it will be more then worth it.
Don't let the negative people turn you away. Although I have never hunted over their during a gun season, the archery season wasn't like I heard. I've been doing the extended archery elk hunt on the Wasatch Front for a couple years now. I heard their was no elk until it snowed, tons of hunters, and the few elk that were their in September were near impossible to call in and could probably tell you the brand of your call if they could talk. I saw the complete opposite. I hunted for 3 days and I saw 4 branched antlered bulls and 6 spikes the first year I hunted and 50-100 cows (tough to tell if your seeing the same cows each day or not). The elk where responsive to bugles and coming into cow calls every morning until they beaded down for the day. I'm use to our Nevada habitat and didn't get a bull due to the thick underbrush blocking my shots. I heard it was a fluke and that it never happens like that, but the next year was even better. I hunted four days and my timing was perfect. The last two days the bulls were bugling all day long. I saw about the same number of bulls, and sizes as the year before but heard bugles in areas where I never got a good look at the elk so their could have been more. I was able to out an arrow in one the last morning.
The hunting was not easy at all. I had to hike about 5 miles every morning to get to my glassing area and if you haven't seen the Wasatch Front, it is steep country. I was putting in 14+ miles a day up and down canyons. From my experience you have to get away from the roads and the hunters if you want to see elk. Where I hunted, the parking area had multiple cars in the parking area every day, and Saturday the parking area was packed but I never saw any hunters where I was (and yes I was in the extended archery area and on public land OnXmaps is a must), and only a couple guys who were scouting for deer.
But this is during the Archery season so the gun hunts could be completely different.