One of the main arguments for the resurrection is often called the "minimum facts of history". That is, a group of facts surrounding the life and death of Jesus that no self respecting historian would attempt to deny. When all of these facts are combined, the only reasonable explanation is that the resurrection is a real historical event.
Credit is due to pastor Mike Winger for putting these facts into a nice little acrostic poem "ALIVE". I'm only going to go into them briefly in this article. These facts are:
A real crucifixion
Ladies found the tomb
Independent appearances of Christ
Violence endured by the Apostles (and confessors in general)
Enemies of Christ converted.
A real crucifixion
That Christ was genuinely crucified is one of the most well attested facts in all of history. If you can know anything about the past, you can know Christ was crucified. As well as the Bible containing 4 independent witness testimonies to this fact, even hostile sources, such as the works of Josephus, testify to this fact. The crucifixion happened, and there is no way Jesus survived it. Obviously, the fact that He died does not prove He rose, but He could not rise if He did not die.
Ladies found the tomb
This may not seem significant in today's culture, but in the culture of Jesus' day, women were not seen as reliable sources. One anti-Christian named Celsus even pointed to the fact that "a half frantic woman" discovered the empty tomb as a criticism of Christianity. In critical thought, there is a principle known as the criterion of embarrassment. That is, accounts which contain embarrassing details are more likely to be true, because it would be counter intuitive for an author to include such embarrassing details. Women being relied on as primary witnesses in a male chauvinist society would certainly be embarrassing, and so it is likely true that the tomb was found empty.
Independent appearances of Christ
Christ appeared to multiple witnesses. Not just one at a time (although that did happen as well), but to multiple witnesses at the same time, ranging from 10 of the Apostles to all of the surviving Apostles to entire crowds of 500 people. Paul even appealed to these people as living witnesses who could be cross examined during his life (1 Corinthians 15:6). Obviously, they can no longer be interviewed, but Paul was writing to people who existed when they did, at the very least revealing his confidence that they all saw something. Unless you want to believe group hallucinations happen (which would invalidate all epistemology, even science, as scientists could collectively hallucinate the results of an experiment), you have to acknowledge that something happened that would convince 500+ people to testify that Jesus rose.
Violence endured by the Apostles
Most people are not even willing to suffer for the truth, much less a lie. Galileo, for example, was forced to recant his heliocentric model under persecution from the Catholic Church. Although it is possible to die for a lie, how likely is it that 12 people would be willing to endure a torturous existence, with no earthly rewards, for something they knew they made up? It makes no sense to suffer violence for what you knew you made up, and so the consistent testimony of the 12, in spite of such violence against them, is evidence that they at the very least believed they saw Jesus alive. On top of the Apostles, other witnesses of Christ were also persecuted. Obviously, if someone who hadn't seen Christ alive still believed it, this would prove nothing, but the culture did not discriminate between those who merely believed Christ had risen and those who actually saw Him alive. The fact that those who claim to have seen Him suffered violence and all refused to recant suggests they sincerely believed they saw Him. The question we are left with, therefore, is why?
Enemies of Christ converted
Aside from the Apostles being consistent in their testimony, some of those who initially disbelieved, and even actively opposed Christ, converted. James and Jude, Jesus' brothers, initially believed He was bonkers, yet they ended up writing scripture. Paul was well known for persecuting the Church, but instead became persecuted for the Church, eventually giving his life for the Gospel. There is no obvious motive for Christ's enemies to lie about why they converted, especially not when this stripped them of their power and effectively put them at the bottom of the societal ladder. Only a genuine experience with Jesus explains why His enemies would claim to have had one.
Taken independently, you could probably pick apart these facts. The explanations for them are usually wild and wacky (some even speculating Jesus had a twin brother who, for some unfathomable reason, wounded himself to fool even his own mother into thinking Jesus had risen), but it is possible to maybe explain one or two facts away. But all of them? Even just these 5 (there are more) are a tough nut to crack, so much so that sceptical historian Bart Ehrman advises his students not to try, lest their Christian friends shred their worldview right in front of them. All available evidence points to one logically consistent conclusion: Christ is risen. If you believe this, as He has given ample reason to do, He will raise you on the last day and grant you access to His Kingdom.