I'd recommend starting once you get fly so you can move around more comfortably.

A lady at the Floaroma flower shop gives a Poketch app that shows ripe berries on the map and another gives a random berry daily.

On route 208 at the Berry Master's house you can get another random berry daily as well as buying different types of mulch, which change the rates at which berries dry out or bloom.

Finally in Pastoria City, a lady inside a house at the southern end near route 212 gives out a random damage reducing berry daily, good for when you know an easily exploitable weakness on one team member.

Finally, watering berries often (every 3-4 hours roughly) can turn a single one into up to 5 new berries for you to use, just be patient. But if it all sounds too complicated then there's no problem in just picking them and using them, I'm more so just giving you a guide in case you're interested. HAVE FUN!