How was Saul of Tarsus saved — did he repent on his own first?

Saul of Tarsus was saved entirely by God's grace, not by repenting on his own first. He was on his way to Damascus to carry out persecution when God knocked him off his horse, spoke to him, and saved him. He did not first come to himself, apologize, or ask to be accepted. Salvation was without his effort.

Les explains that Paul is the epitome of a sinner saved by grace. Saul of Tarsus had every right in the world to be zapped, but God showed him mercy. Saul did not suddenly come to himself and repent, saying, “Oh, God, I’m so sorry. Won’t You please accept me?” Instead, while on his way into Damascus to carry out his dirty work, God literally knocked him off his horse and spoke: “Saul, Saul, why persecutest thou Me?” That was grace. Les teaches that every believer is a vessel of mercy, saved without ever doing anything on their part; it has always been this way.

Romans 9:24

Even us, whom he hath called, not of the Jews only, but also of the Gentiles?

Are we saved the same way the Apostle Paul was saved?

Yes. Believers are saved exactly as Paul was: by God's grace and mercy, not by our own repentance or works. God took the initiative with Saul of Tarsus, and Paul became the epitome of a sinner saved by grace. We are in that same category, saved without ever doing anything on our part.