How did each of the 12 original apostles die, and where are the records of their deaths found in the Bible?
The New Testament, for the most part, was written by the apostles or those close to them. As such you would expect the records to end before the authors died, and such is the case. Only the deaths of two of the apostles are actually recorded in the Bible. We frequently overlook that Judas Iscariot, though he betrayed the Lord, was one of the twelve apostles. He committed suicide by hanging himself. "Then Judas, His betrayer, seeing that He had been condemned, was remorseful and brought back the thirty pieces of silver to the chief priests and elders, saying, "I have sinned by betraying innocent blood." And they said, "What is that to us? You see to it!" Then he threw down the pieces of silver in the temple and departed, and went and hanged himself" (Matthew 27:3-5). James was the next apostle to die, being beheaded by Herod. "Now about that time Herod the king stretched out his hand to harass some from the church. Then he killed James the brother of John with the sword" (Acts 12:1-2).
Beyond this, two of the writers mention that their time of death was coming soon. Paul mentions his pending death, "For I am already being poured out as a drink offering, and the time of my departure is at hand. I have fought the good fight, I have finished the race, I have kept the faith. Finally, there is laid up for me the crown of righteousness, which the Lord, the righteous Judge, will give to me on that Day, and not to me only but also to all who have loved His appearing" (II Timothy 4:6-8). At the time of this writing, Paul was in prison in Rome, so it is probable that he died at the hands of the Romans. Peter also mentioned the nearness of his death. "Yes, I think it is right, as long as I am in this tent, to stir you up by reminding you, knowing that shortly I must put off my tent, just as our Lord Jesus Christ showed me. Moreover I will be careful to ensure that you always have a reminder of these things after my decease" (II Peter 1:13-15).
What remains is a set of traditions and writings by early Christians which gives us clues as to what happened to the remaining apostles. Since these are uninspired works, we cannot be absolutely certain as to their accuracy. John Foxe, in 1563 A.D. published a famous book, Foxe's Book of Martyrs, which includes the believed outcomes of each of the Apostles. It is probably as accurate as any other book of history written by man.