Though you will already have a number of traversal abilities in Hollow Knight: Silksong, getting the actual Double Jump isn't easy. Called Faydown Cloak, this adds to your arsenal, which should include Silkspear, Dash, and Clawline.
You will need get all the way to the top of Mount Fay, which has a few difficult conditions: it's cold there so you will need to find warming points; there's few enemies so less healing for you; and there are hardly any benches.
This area is connected to The Slab, so you need to get there first (accessible from Choral Chambers).