If a man and a woman married to a different man have sexual intercourse, they are both liable to the death penalty by strangulation (Leviticus 20:10; Mishna Sanhedrin 11:1).
The death penalty has not been administered since the Sanhedrin left their court room on the Temple mount in the years preceding the destruction of the Second Temple in Jerusalem (nor can it possibly resume until they return there) (Bavli Sanhedrin 41a).
The standard of evidence is two (Deuteronomy 7:6) adult, male, non-related, non-sinning (Exodus 23:1) witnesses who warned the violators immediately prior to their sin that they would be killed by strangulation. The witnesses do not need to see, to use the Talmud's (Makkot 7a) analogy, like a eye-color brush in its tube, but rather to see them acting as lovers do (Rambam Issurei Biah 1:19). However, the Mishna does record (Makkot 1:10), that any court which can't find a way to exempt all cases but at most one in seven (some say seventy) years is a murderous court. Suffice to say, such executions were not at all common.