First and foremost is understanding the basic needs of elk and how it relates to the time of year you are hunting, and the area you are hunting in. Elk like thick bedding cover and cooler temperatures, however, their bedding areas can change when winter temps start to push the mercury down.
Biologically elk try to preserve calories and limit the buring of fat reserves. Winter is a serious time for elk and if to many reserves are burned, they will die, and they know it. As a hunter, you want to look for bedding area that are closer to food sources as the temperatures start to drop, however, cover is still important to escape predators during the hunting season.

In general, there are some basic observations that can be useful. I like long ridges with multiple fingers coming of of them. The main ridge is typically a great crossing and traveling route for elk. Additionally, they can find water sources along these micro drainages between fingers and thick cover for hiding out. Also, the top 1/3 of the mountain will hold the most elk. Understand too, that after the rut the bigger bulls are gone, they leave the herd and get out of there. I have seen many guys chasing a herd around only to discover there is not a legal bull in the bunch. So it is good to know before hand what you intend to hunt, cows or bulls. All of this, of course, depends on the time of year.

If I were scouting I would capture a long ridge with multiple fingers on my map work. Hopefully this ridge is away from the roads at least a little bit. I would walk down the ridge looking for fresh sign, old sign does no good. Too many hunters spend too much time in areas that "had" elk in it, or looks like "good elk habitat". If you are not finding fresh sign, you are hunting were they elk are not, big mistake. Lets say you see fresh tracks, fresh dropping etc. Ok, now you know they elk are in here. From this point on, it is really a matter of spotting the elk. You need to uncover their bedding areas and feeding areas. Feeding areas will contain nipped of grass and beds out in the open. Remember, elk also bed at night, so finding beds in open grassy areas is a good indication that they are feeding in this area. Once you have uncovered bedding areas and feeding areas, the next step is too route transition zones. These transition zones give you your best chance to harvest an elk during rifle season. These are the areas the elk move through enroute to feeding/bedding. Also, you need to establish at what time of day they are moving. If they are in their bedding areas before light, you'll need to get there first and wait, if not, get closer to the bedding area to take advantage of early movement.

As humans we have a tendacy to glass open areas, however, while it is in our nature, it isn't the most effective way. Lets say you are setting up next to a bedding area in a transition route in the evening. You glass work needs to be focused on the thick stuff were you expect the elk to come out. Really look hard into these areas and pick up the elk instead of glassing the more open country. Elk like to bed on north slopes toward the top of the ridge. They can catch thermals coming up, see danger below as well. If spooked they can and will roll right over the ridge and get quickly out of sight. So if glassing for bedded elk, look hard towards the upper portions of the ridges. Often time you will find an old bull in a thick clump of stuff with open lanes for watching below, use this to your advantage. While they like to have some visual lanes, they rarely lay out in the open unless it is cold. However, these lanes also provide you the glasser with an opportunity to catch them. Generally, the colder it is, the more elk like to be out in the open catching the suns rays.