Dear Br. Ahmed: Assalamu Alaikum.. Two separate issues were confused in your question. Adultery (i.e. sexual intercourse with someone other than someone's legal spouse), is prohibited in Islam. If a person committed adultery he/she will be punished by the Muslim government that have immediate jurisdiction over the county he/she lives in. The second issue, of bringing four credible witnesses in court, is applied when a person accuses a chaste woman who is a believer of committing adultery. The accuser has to bring four witnesses to support that they saw the woman actually involved in sexual intercourse with someone who is not her husband. If the accuser does not have witnesses, then he/she would be lashed eighty (80) times and any of his/her future testimonies will not be accepted thereafter. I hope this clears your confusion. About the criteria for witnesses, Islam defines a strict criteria for witnesses for any legal matter. For example, a witness should be a truthful person that never lied in his life. I hope this briefly answers your question. Thank you for participating with your question. Assalamu Alaikum.
(Source: IslamiCity) Classified in Adultery > the islamic ruling on it