"can you hunt elk like we hunt deer"
As a resident of Wyoming, we can buy an over the counter tag called a general. This is good for Elk in any area trat allows a general tag. Some elk areas are drawing only. Then there are the different type of licenses, but you can look that up on the G&F site.
We can get up to two elk tags. One would be the general or drawing only tag, in addition to that, there are some areas where they issue a Type 6 tag (drawing only) for cow/calf only - NOT "antlerless".
So we can legally take two elk a year if the elk gods are with us.
Harvest success for elk nationally is one in five years. For me, I do a little better than that, but I'm a meat hunter first and trophy second. I think 20% of the hunters harvest 80% of the elk. Some major reasons, they know the area they are hunting. They stay flexible in their location and tactics. They scout their area throughout the spring andsummer. And it doesn't hurtif you canhunt on private land, hunting pressure, or the lack of it, can strongly determine sucess.
I think a lot of a hunters lack of success is lazyness. "Tree stand" mentality doesn't work for elk. You can't sit n a trail or wallow for a week and expect to be successful. Elk just aren't programmed that way. They are movers. Originally plains animals, they are programmed to move. When they get into their "elk trot" you can forget about it. They can go all day and easily cover 20 miles while you are still huffing and puffing to get over that next ridge!
One last thing that I see a lot in both archery and rifle, is dead - untagged Elk. If you shoot, don't quit looking for it. They can go for miles with a hole in them.
I get a little windy when talking about elk. Sorry. Your other ??? was about getting tags every year. Yes, the general tags for residents. Non-residents must apply for an area every year and success rates vary. But consider the "leftover" drawings later in the summer and the Type 6 way to go also. Between all of those options, a guy could expect to get some kind of elk tag every year. And if you don't, there's always Colorado.

Good hunting . . .