This is going to sound like a smart a$$ answer but it is not. Hunt where the elk are. If you are talking about Colorado (which I assume you are) they have been been through and archery season, muzzy season and one rifle season before the second season. Be willing to go where no man wants to go. The elk will gather in places that nobody bothers them. You may get a chance at them early in the morning or late evening but, by the middle of October they are well conditioned. We have been lucky enough to get new elk pushed into our area that don't seem to know where the safe zones are for a day or 2 and have had good success.
That's all good advice from Bull Buster. Try to envision where pressure will come from and where it will send the elk. You'll want to find natural choke points and escape routes to take advantage of. If you think you'll be hunting unpressured elk, you'll want to hunt whichever habitat factor is in the least abundance; water, food, cover.
The best thing to do that time of year is get high depending on the snow fall level and have some excellent optics and really glass. You want to glass out to 4 or 5 miles if you can with a good spotting scope. The elk will be pretty quiet so glassing will be the key. Be prepared to do a lot of walking moving from different peaks glassing below drainages but the hunt really should be divided into two phases. The first phase is you aren't necessarily going to be where you think elk are. You want to be finding good vantage points and glassing like crazy. Once you've located elk then phase two comes into play and thats where you formulated how you're going to go into the area and hunt.
The older I get the more I get away from going into the timber and looking for sign and the more I go to glassing from high vantage points out several miles. You would be surprised at how much you learn about an area doing this.
I could see the small band of mule deer picking their way towards me through the sagebrush 800 plus yards away. With my 10 power binoculars I spotted a legal buck bringing up the tail. I dropped down and crouched behind a large chunk of sage just waiting for them to pass within range. Unfortunately, they stopped and began milling around before finally settling down, with a few of them laying down right out in the open. They were not going to come to me; if I wanted any closer, I'd...