Instructions
Play a game of Blitzball. The team lineups don't matter as long as Tidus is one of the members of the opposing team. You can't learn Tech Shots from players on your own team.
Wait for Tidus to perform his Sphere Shot. You will see a message indicating that he is about to do it, so pay attention any time Tidus has control of the ball.
Watch the slot machine-like display that appears on-screen. This is how the bonus to the shooting power (SH) of the shot is determined. Listen carefully here -- you will hear a chime as soon as the bonus is determined and just before Tidus' foot kicks the ball. Press "X" immediately after you hear the chime to Techcopy Sphere Shot.