This is a really fun adventure through beautiful terrain. If you don't like ski areas, you might be bugged by a couple miles that go through the bottom of Vail, but it's still quite remote and peaceful.
The Two Elk trail is very steep and much harder on the east end (from I-70 up to Two Elk Pass). The western portion is considerably easier. Most people travel in the east to west direction, arranging for a shuttle pickup and/or drop off.
To get to the start of the Two Elk Trailhead, you must park at the Deluge Lake
trailhead and hike 1.8 miles up the Old Vail Pass road, now called the Vail Pass Recreation Path. The junction with the true Two Elk Trailhead is on the right in a large clearing. The trail drops from the recreation path to a bridge crossing the Black Gore Creek, then passes under I-70 into the tight Timber Creek canyon which is a cool, shady forest alongside the creek. At mile 2.6, the trail makes a sharp right across a third bridge before starting the steepest climb up to Two Elk Pass. From the pass, you can take in views of the Gore Range, Sawatch Range, and Vails Back Bowls.
At Two Elk Pass, a bunch of trails diverge. Don't worry too much as long as you're on one that is going downhill to the west, below the Mongolia bowls of Vail ski area and towards the base of Orient Express (#21) and Teacup (#36) chairlifts. There is evidence of an older version of the Two Elk trail that is deeply rutted and goes straight down the drainage. The new trail is now very smooth, easy, well built, and winds around the open meadow.
Continue down, passing the bottom of ski lifts. You'll cross a few roads, but never stay on one for more than 100' or so, and you'll find the Two Elk path again. You might have to look around in a few places, but it's all there. Once you leave the ski area behind you, the forest gets thicker and the trail rockier. It follows Two Elk Creek for several more miles of moderate to difficult hiking (due to rocks) until eventually popping out at the valley floor.
You'll be at the end of Cemetary Rd (and a shooting range, which is a little disconcerting after so many miles of backcountry hiking). Pick up your shuttle ride here or follow the road for a mile or two into Minturn.