What is the ruling on obtaining a forged certificate of experience for money to use for work, and how does one repent from that?

What you have done is false testimony and is impermissible, due to the Prophet's (PBUH) saying: "Shall I not inform you of the greatest of grave sins? False speech" — or he said — "false testimony." Therefore, you must repent and seek forgiveness. If you are capable of teaching the subject, then nothing more than that is required of you. But if you are not capable, then inform your employer of the truth of the matter. If they approve of you, then stay; otherwise, do not.