NKJV - 43 And Jesus said to him, "Assuredly, I say to you, today you will be with Me in Paradise.
For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
Paradise is under the earth. Jesus went to paradise when He died. Abraham went to paradise. Under the earth. The center of the earth is divided, hell on one side, and paradise on the other. When Jesus went to paradise He took all of the Old testament saints out of paradise to heaven. Now, when those of us who are saved, die, we go right to heaven.
Remember when the rich man died. He could talk to father Abraham across the chasm between paradise and hell.
So, when Jesus said, today, you will be with me in paradise, that is exactly what He meant. The thief was saved just by believing Jesus was who he said he was. He professed his faith when He said, remember me when you come into your kingdom. He recognized Jesus as God. He believed on Him. That thief is in heaven now awaiting the resurrection of his new body.
Romans 4:5 But to him that worketh not, but believe on Him who justifieth the ungodly, his faith is counted for righteousness. Romans 4:6-8. We are given eternal life by faith alone in Christ alone.
That thief turned preacher. He proclaimed Jesus was the Christ, the savior of the world to all who believe on Him. He was saved by faith alone without works.