How does a person know that Jesus died for them? The answer is because scripture says so. Our salvation is assured on the works of our Lord and Savior, Jesus Christ. God says when we trust in Jesus' death, burial, and resurrection, we are forgiven and saved.
John 1:29 The next day he saw Jesus coming toward him, and said, "Behold, the Lamb of God, who takes away the sin of the world!