You should have learned on the Sphere Grid, which you should have done by now. If you didn't, you may have to go back.

In order to cast it, you have to go to Tidus' White Magic menu in battle, and find the spell called "Haste" and choose a target. As of right now, no, there are no ways to cast Haste with any other characters, get Haste as an Auto-Armor ability, or anything else (since you cannot customize as of yet).