Yeah, no equipment required - you can jump up there immediately on arrival, though you need the morph ball and bombs to clear the passageway (I'd already nuked it before recording that gif). Both items are acquired a few minutes into the game, ofc.
For walljumps, you need to be in a spinning jump (jump while moving forward), make contact with a wall or ledge, hit and hold "away" and a moment later hit jump. The delay between those two inputs takes getting used to, but the window is pretty forgiving (wait for Samus's turning frame, seen in that gif). With practice it's easily possible to walljump straight up sheer walls, making SM goddamn catnip for me and my affinity of sidescrollers with the mechanic. ^__^ I'm not even bothered about Fusion and to a much lesser extent ZM's linearity. Between the engine and geography SM's already got a lifetime's worth of stuff to try out.
As Roo said earlier in the thread, technically you're meant to learn walljumping after falling into a vertical shaft with friendly walljumping animals (or letting the demos run long enough to play the scene), but the crucial delay between "away" and jump isn't quite obvious. It'll feel godawfully inconsistent if you're hitting the commands simultaneously. It's also critical to not hit any directions besides "left" or "right" ; AFAIK, anything else will break the spin. Not sure if that can be counteracted - I like how Fusion and ZM let you start a new spin at any point by hitting Jump in midair.
I find bombjumping a bit squirrely in the original and Super (it was chopped right out of Fusion), but I've not put the time in. ZM's massive blast radius is EZ modo, at least for vertical ones. Horizontals still perplex me a bit. Just barely got the early Varia suit then called it a day pending further practice.
edit: CRUMBZ I WAS (and indeed still am) TIRED AND DRUNK, apologies if you already know about walljumping Ed! 3: I seem to recall springing a possibly unsolicited tutorial on someone else recently, it's the booze talking I swearz ;3 ;3 ;3
the booze and the walljumps D:
<- muh brain