The main source is Livy's History of Rome since the Foundation 8.17.8-10 (referring to the year 332 VC = 329/328 BCE) and 8.24 (referring to 326 VC = 323/322 BCE, but in fact 331 BCE). The two sections are offered here in the translation by B.O. Foster.
[8.17.8-10] Samnium likewise had now for two years been suspected of hatching revolutionary schemes, for which reason the Roman army was not withdrawn from the Sidicine country. But an invasion by Alexander of Epirus drew the Samnites off into Lucania, and these two peoples engaged in a pitched battle with the king, as he was marching up from Paestum. The victory remained with Alexander, who then made a treaty of peace with the Romans; with what faith he intended to keep it, had the rest of his campaign been equally successful, is a question.
[8.24] It is recorded that in that same year Alexandria in Egypt was founded, and that Alexander of Epirus, being murdered by a Lucanian exile, fulfilled by his death the oracle of Jupiter at Dodona. On his being summoned to Italy by the Tarentines, the oracle had warned him to beware of the Acherusian water and the city Pandosia, for there he was destined to end his days. On this account he had passed over with the more speed into Italy, that he might be as far removed as possible from the city of Pandosia in Epirus and from the river Acheron, which, debouching from Molossis into the Infernal Marshes, discharges its waters into the Thesprotian Gulf. But, as generally happens, in seeking to escape his doom he ran full upon it.Having repeatedly defeated the Bruttian and Lucanian levies; having taken Heracles, a Tarentine colony, from the Lucanians, and Sipontium belonging to the Apulians, and the Bruttian towns Consentia and Terina, and after that other towns of the Messapians and Lucanians; and having sent to Epirus three hundred illustrious families, to be held as hostages, he took up his station not far from the city Pandosia, which looks down upon the borders of Lucania and Bruttium, on three hills that stand some little distance apart from another, that he might thence make incursions into every quarter of the enemy's country. He had about him some two hundred Lucanian exiles, whom he trusted; but their loyalty, like that of most men of that nation, was prone to change with the change of fortune.
Continuous rains, which flooded all the fields, having isolated the three divisions of the army and cut off from mutual assistance, the two bodies other than the king's were surprised and overpowered by the enemy, who, after putting them all to the sword, proceeded with their entire strength to blockade Alexander himself. Whereupon the Lucanian exiles sent messengers to their countrymen, and promised that, if assured of restoration, they would give up the king, alive or dead, into their hands. But Alexander, with a chosen band, made a daring attempt, and broke out through the midst of his foes, cutting down the Lucanian general in a hand-to-hand encounter.
Then, rallying his followers, who had become scattered in the flight, he came to a river, were the fresh ruins of a bridge, which the violence of the current had swept away, pointed out the road. As his company were making their way across the stream by a treacherous ford, a discouraged and exhausted soldier cried out, cursing the river's ill-omened name, "You are rightly called the Acheros!" When the king heard this, he at once bethought him of the oracle, and stopped, undecided whether he should cross it or not. Whereat Sotimus, one of the young nobles who attended him, asked him why he hesitated in so dangerous a crisis, and pointed out the Lucanians, who were looking for a chance to waylay him. With a backward glance the king perceived them at a little distance coming towards him in a body, and drawing his sword, urged his horse through the middle of the stream. He had already gained the shallow water, when a Lucanian exile cast a javelin that transfixed him.
He fell with the javelin in his lifeless body, and the current carried him down to the enemy's guard. By them his corpse was barbarously mangled, for they cut it in two through the middle, and send a half to Consentia, kept the other half to make sport for themselves. They were standing off and pelting it with javelins and stones, when a solitary woman, exposing herself to the inhuman savagery of the raging crowd, besought them to forbear a little, and with many tears declared that her husband and children were prisoners in the hands of the enemy, and that she hoped that with the body of the king, however much disfigured, she might redeem them. This ended the mutilation.
What was left of the corpse was cremated at Consentia by the care of none other than the woman, and the bones were sent back to Metapontum, to the enemy; whence they were conveyed by ship to Epirus, to his wife Cleopatra and his sister Olympias, of whom the latter was the mother, the former sister, to Alexander the Great. This brief account of the sad end of Alexander may be excused on the score of his having warred in Italy, albeit Fortune held him back from attacking the Romans.