You want to press jump a little bit after you press the D-pad in the direction away from the wall. The time you have to do varies but you have between two and ten frames to do this. Don’t try and press them at the same time or it will always fail.

Are you a visual person? This image might help. You want to press jump when Samus is in this position, almost sitting against the wall.

Here’s a video of someone wall jumping with a controller overlay so you can see their inputs and compare it to what’s on screen.

It might take a bit to get the timing down but once it’s in your muscle memory it is very consistent. If I can do this then anyone can do this.