tá sé ag rá a phaidreacha - he is saying HIS prayers

caithfidh Ciarán fanacht lena sheal - Ciarán must wait HIS turn

can anyone tell me how you know which form of "his" you use and whats the difference??

Just as you say "wait for" in English, you say "fan le" in Irish. Le is a preposition, and when it combines with a you get lena.

Other combinations:

de + a = dá
do + a = dá
faoi + a = faoina
go + a = gona
i + a = ina
ó + a = óna

Basically, whenever the preposition ends in a vowel, it combines with a and other possessive adjectives that start with a vowel.