Energy drinks restore 30 AP, but they're not available for purchase at the start. You can get one from a traveling drinks merchant who might stop by your house in the evening, if and only if you buy something from him (he sells tea, coffee, and snacks, at a discount).
Green Tea restores 10 AP, and Black Tea restores 5 AP.
If you're asking about raising max AP, then these actions will raise max AP:
- doing basic training at the guild
- after-hours training with guildmates (also raises their stats)
- part-time work at the farm on weekends
- Voluntary Training --> Run (only available on weekends, before dinner)
- Great Adventure with Imouto on weekends (also raises your other stats)
I think it's also possible to raise max AP by doing Contribution and Subjugation at the guild, but I'm not 100% sure. I know they'll raise some of your other stats, though.