From a spin jump, a shinespark wind-up is triggered by releasing either forward or jump (or both) and pressing either up or angle-up.
The wind-up' is a brief period during which the player can control the direction of the spark.
During the wind-up, if jump is pressed together with up, angle-up, or forward, Samus will immediately spark up, diagonally, or horizontally, respectively.
If the wind-up expires, Samus will default to a vertical spark.
If jump is held when activating the wind-up by pressing up or angle-up, then the wind-up is effectively skipped as the spark activates immediately.
For a mid-air horizontal spark (the trickiest case), the sequence is to spin-jump, release jump, tap up or angle-up to activate the wind-up, then press forward and jump to spark;
it is also possible to hold forward the entire time;
either way, the important points are to be sure to release jump before activating the wind-up,
and be sure to release up/angle-up (pressing forward instead) before repressing jump to activate the spark.
The wind-up period is fairly lenient, so the timing of the jump input after the up/angle doesn't need to be rushed.
Note that mid-air shinesparks can't be performed from a fall, only from a jump.
See also: Tech Page