The north trail starts at trailhead just past the Halfmoon Lake Campground on Forest Road 110 (from Leadville: south on 24, right on CR300, left on Halfmoon Road, right on FR110; totals 11.5 miles from leadville).
The trail is very well defined the entire way to the summit, and is often referred to as the standard route. It starts as Trail 1776 for about a mile, then bang a right on Trail 1484 (it's marked, but the sign is washed out, but it's pretty obvious--just go up the mountain at this juncture).
It's 4.6 miles from trailhead to summit. There's a steep section just prior to treeline, and a steep route-finding section (sketchy if you're not wearing hiking boots) from about 12,500 to 13,500. But you can wear sneakers and do just fine.
The major drawback to this route is that you never see the summit until you get to the last false peak (where there is a large cairn) just 1/3 mile from the summit.
But this route's trailhead is easier to get to by passenger car than the upper trailhead on the South Trail, so if you don't have a high clearance vehicle, you'll want to do this route.
I don't know what route is described in this route description, but the north trail has been there a long time and has been climbed by thousands over the years.