Please look at the NPS website for Guadalupe Mtns NP for trail descriptions. This is my impression of the hike.
Make sure you wear hiking boots and have plenty of water - there is no water available other than at the trailhead.
There are three portions of this hike - the Pratt Lodge, The Grotto and The Notch. If you go all the way to The Notch, you will see all three sights. The first portion to Pratt's Lodge is fairly level and relatively easy to hike on mostly gravel/rock, nice wide trail in most places. The second leg to The Grotto/Hunter Line Shack is mostly level and a mixture of dirt and rock. LOTS of Fall color when I hikes and the main reason I wanted to see the canyon. At The Grotto, there are tables to relax at.
Prior to going to the notch, the trail branches left to The Grotto and right to The Notch. When you go right, you will be on a series of switchbacks going mostly up for about 1.75 miles. The trail is rocky but as you climb higher you can see down the canyon quite a ways. When you get to The Notch, the trail continues on the other side of the crest but I didn't go any further. The attached photo shows the view of South McKittrick Canyon from The Notch.
This route was very enjoyable and this hike was one of the reasons I went to the park. Nice Fall colors as well!