Ah, the good ol' cow hunt. I'm an unrepentant cow hunter and have been fortunate enough to take about dozen myself and lead my older two kids to two apiece (so far).
TboneAZ of this site has been very successful hunting cow elk in AZ; hopefully he'll stop by and impart his wisdom as well.
Have you hunted other big game before? What kind of experience and gear can you draw on?
Long shot perhaps, but consider teaming up with other hunters who have hunted elk before. Elk hunting can be a time and gear intensive pursuit. If you can tag along with an experienced hunter or two, you'll have access to knowledge and gear. This will help you learn how you like to hunt elk and what kind of gear that requires. You can walk and stalk, hike way back in, drive around, glass and stalk, and so on. Lots of methods that require different skill sets and gear.
Research draw odds and success rates for game units in which you have an interest. Talk with the game and fish about those units and first-timers. Focus on units that have relatively decent draw odds and success rates, at least to start.
My experience is mostly with later season cow hunts after the rut. Bulls are in hiding and the cows are grouped up in herds of 10 to 50, sometimes more. If you get a chance to visit the areas you're interested in during the approximate seasons, you can get a feel for the areas elk like to be. Scout for good sign (tracks, droppings, travel lanes, feeding areas, bedding areas, and so on). Be out moving at first and last light and try to actually see elk. Where are they coming from and where are they going? Can you get between where they are and where they want to be? Can you spot elk feeding in areas that are stalkable? Can you determine where they bed, and if so, can you still hunt those areas with a realistic chance of sneaking up on them?
One of my favorite ways to hunt late season cows is to find fresh tracks in the snow early in the morning. Those are usually tracks of elk going to bed. Assuming the wind is right, get on those and follow. Many times you can catch up to slow moving elk while they're still puttering around in the trees. Elk will often browse their way to bed, so they'll be up making noise. If you're a decent stalker, you can sometimes follow along and ease within range of the feeding herd before they make it to bed, where they lay quietly and alert.
That's just a start. There are many ways to chase cow elk. The hardest part is getting a tag in a unit with a decent population that will give you several opportunities to screw up, then finally get it right.