Dua when it begins to rain and after rain

اللَّهُمَّ صَيِّبًا نَافِعًا/اللَّهُمَّ اجْعَلْهُ صَيِّبًا نَافِعًا
O Allâh! (Make this rain) abundant and beneficial.
(Bukhari, Nasai with the words اجْعَلْهُ)

AFTER IT RAINS
مُطِرْنَا بِفَضْلِ اللَّهِ وَرَحْمَتِهِ
We have been granted rain through the grace and mercy of Allâh.
(Bukhari, Muslim)