Be careful of this one (certainly on Vita). I got hosed out of it, and the best I can tell is it's because I leveled a spell to 2 before finishing getting everybody's Level 1 spells. So,
do not get level any spell to the second tier until you've bought all of the first tier spells.
Outside of this glitch, it's pretty easy. Whenever the group goes up a level, a new spell point is awarded. Spend them at the airship. A yellow exclamation point will appear over the spell giver's head when points are available. Don't forget to horde your points if a level 1 spell is still blocked off based on the character's level. It's clear in the menu, so this shouldn't be an issue.
Edit: So, I went back through with a fresh save on Vita and PS4, avoiding purchasing any level 2 spells and it still didn't pop. I did find a solution posted elsewhere. As I don't want to take credit for other people's work, I will just post the link:
https://www.playstationtrophies.org/forum/dungeon-punks/3029...Sorry to force a click out. The solution does work, at least.