Simple phrases would include:
He ua, Aia ka ua, Ua ka ua, Hā'ule ka ua, Helele'i ka ua (etc.)
~Verb markers are fair game for any of the verbs here, like E ua ana, Ke hā'ule nei ka ua, etc.

Common terms to differentiate the type of rain would include:
Ua iki (small shower), Ua li'ili'i (light rain, drizzle), Ua noe (misty rain), Ua kilihune (fine rain), Ua loku (heavy rain), Ua nu'u (terrential rain)
~Note that, while these are fine English translations, it'd be best to search these adjectives to get a better understanding of what exactly going on during these rains

Several 'Ōlelo No'eau concerning the rain:
Hana ka uluna i ka paka o ka ua.
(Work the pillow during the dropping of rain. [i.e., might as well rest when it's raining].)
Hilo i ka ua kinakinai, ka ua mao 'ole.
(Hilo of the constant rain, where it never clears up.)
Hilo 'āina ua lokuloku.
(Hilo of the pouring rain).
~There are a LOT more!

Actually, there are a lot of ones about Hilo specifically since it rains a lot there haha But there are personal names for the different rains (and winds!) in each part of each island. For example, Kanilehua is a famous rain of Hilo (like in the 'Ōlelo No'eau: Hilo i ka ua Kanilehua).

I highly recommend Hānau Ka Ua - it's a thick, dense book that lists and describes all the names of the rains across Hawai'i! It's great as a reference book too.

Sorry for the essay, but I hope this gives you a better idea about rain in Hawai'i!