The poem opens by making clear that the "Climbing" of the title, though unusually combined with "Grandfather," does relate to a kind of mountain climb. The speaker feels that it is important to make this climb "free, without a rope or net." That is, they see what is coming as something that requires effort, an element of risk, and determination.
The fact that the poem opens with the first person singular pronoun, "I," makes it clear that this is a personal poem—one in which the speaker will attempt metaphorically to explore the memory of their grandfather through the imagery of a mountain climb. And though perhaps it is not revealed yet, the reader gets the sense that the speaker sees this as an important mission worthy of undertaking.
The climb itself, then, begins at the base: the grandfather's shoes. These shoes are a "dusty and cracked" pair of brogues, which are a rather old-fashioned shoe (signaling the grandfather's age). The phrase "dusty and cracked" also hints at the way memories deteriorate and change. Indeed, part of the poem's purpose is to keep this particular memory fresh and vivid, even if it is surreally adapted to the imagery of a mountain climb.
The sibilance in line 2 has a dusty sound to it, which is picked up in line 3 and creates a sense of slipperiness—though this is still the easiest part of the climb:
First, the old brogues, dusty and cracked;
an easy scramble onto his trousers
In these first few lines, the speaker focuses their attention on the clothing of the grandfather, partly because the speaker has not yet reached high enough to find the grandfather's features, but also because this is the way that memory works. That is, certain details come back first, and show the way to the more intimate and affectionate aspects of a memory (ultimately, the grandfather's face and "the slow pulse of his good heart").