I just started elk hunting myself 4 years ago when I moved here to Idaho. The first year was a real learning experience. Idaho probably has terrain closer to western wyoming in that it is STEEP. So your mileage may vary depending on what state you decide to hunt:
1. Get away from the roads and the trails. Elk are sensitive to pressure and any road is bad, but many popular atv, horse or hiking trail can have the same effect. Our main huning hole which produces multiple elk every opening day is only about 1 mile from a busy road, but the elk are two ridges and about 1500 verticle feet away, so they feel safe. Pressure is limited because new people come in shoot an elk then learn that packing 1.5 miles and 1500' elevation UP, is no fun and don't come back.
2. What time of year you hunt will change tactics a lot. Early season, typically bow hunting, the elk rut, which is a major advatage. Just after the rut, typically early-late Oct, the bulls go and hide. This is when most general hunts are and the bulls can be real tough to find. After Nov 1, the elk start to herd back up and move. I find this to be my favorite time. The key here is, unlike deer, elk aren't everywhere, so you have to find the ridge or drainage where they are and hunt there.
3. To find elk in mid or late season you need to be very lucky, or you must have and use some decent Optics! In S. Idaho you can see a long way, as can the elk, so glassing is what has made the biggest difference. Getting a shot off on a suprised elk ain't easy so knowing where they are and planning a stalk is a key to success so, GLASS GLASS GLASS.
4. If you kill one, DO NOT underestimate the work involved. An average sized elk is a lot of work. I hunt on foot and use horses to pull elk out of the woods. Again Idaho is steep so even downhill is difficult, uphill is just cruel. So, be prepared as you need the right gear: a good knife(or two) and sharpener(that you know how to use), parachute cord, game bags, and frame pack(or quality internal frame) you know can handle large heavy loads. I would look for a spot to have your horses by the truck/trailer, hunt into rough country daily, and use the horses to haul out the elk, but with fuel prices today and your limited budget I might just be prepared to get real tired.
If you get into it you will start to spend money, especially if you become addicted to this site. But if you start with a good gun, good basic equipment, a pair of 8x bino's and spotter w/ tripod, then you can kill and bring home elk. GOOD LUCK!