Slavic paganism is the least documented of the major European pre-Christian religions, because no Slavic people wrote its mythology down. Everything comes through outsiders, or through Christian clergy recording what they were suppressing, and for Perun the whole reliable dossier is short enough to summarise here.
Procopius, writing at Constantinople in the sixth century, says of the Sclaveni and Antae that they hold one god, the maker of lightning, to be the lord of all, and that they sacrifice cattle to him. He gives no name. The Rus-Byzantine treaties preserved in the Primary Chronicle under the years 907 and 945 record the oath formula of Oleg's and Igor's men: they swore by their weapons and by Perun their god, and by Volos the god of cattle. The Chronicle then records under 980 that Vladimir set up idols on the hill outside his hall, Perun first among them, of wood with a head of silver and a moustache of gold, and under 988, after his baptism, that the same idol was pulled down, tied to a horse's tail, beaten by twelve men with sticks, dragged to the Dnieper and thrown in, with men detailed to push it off the banks until it had passed the rapids.
That is close to all of it. Add place names across the Slavic world built on his, a scatter of later folklore, and the etymology linking him to Baltic Perkunas and to a root meaning to strike, and the case for a widespread Slavic thunder god is solid. What is not solid is the detailed mythology that fills popular accounts. The elaborate duel between Perun and Veles over cattle, wife and waters, resolved by the thunderbolt, is a twentieth-century reconstruction assembled by Ivanov and Toporov from folklore and comparative Indo-European material. It may be right. No medieval source tells it.