Listening to the Rex Factor podcast it's striking how easily Anglo-Saxon Kings seemed to be able to change wives when they wanted to. Was this true for non-kings as well? If so, do we know anything about how the process worked?
Unfortunately, given that this is more 'public' history, we don't really have any sources as to how the situation played out in practice, but in theory at least, it was relatively easy given a specific set of criteria were met.
The 10th Century penitential known as the Scriftboc contains some of the following provisions under which the Church would allow divorce and remarriage:
A holy union may (not) be divided without the consent of both parties. Either of them may permit the other to join a monastery and take another companion for himself if they were in their first marriage. According to the Greeks it is nevertheless permitted if it is the second marriage. Neither of them may have a third partner as long as the man or the woman lives. If a man has a third wife, both of them must fast two days each week, and during the 3 40-day fasting periods neither one of them may eat meat... If any man or woman promise that he (or she) will remain a virgin and after that joins in lawful wedlock, let neither of them forsake that (i.e., the marriage); (and) they should fast for 3 winters. For foolish vows and those that cannot be kept will be broken.
Infidelity was, naturally, frowned upon:
If anyone's wife commit fornication, the man may leave her and take another if that was his first wife. If it was his second or third wife, he may not then take another wife. If that woman wishes to do (penance) for her wicked deed, after 5 winters she may take another man. If a woman's husband dies, twelve months afterwards she is allowed to take another husband. Whichever husband forsakes his wife and joins himself in adultery, he is to fast a hard fast 7 winters or 15 (winters) more lightly. Whoever it is who does many evil deeds, in murder and fornication with beasts and with women, he is to go into the monastery and fast until the end of his days, if he has done very many evil things.
Whoever it is who is in an illicit intercourse or marriage, nevertheless one is allowed to eat whatever food that he has, for the prophet said: "The earth is the Lord's, and the fullness thereof." Concerning a man and woman who were joined in lawful wedlock, if one wishes to be God's servant and the other does not, or if either of them is unwell and the other is well, then, with mutual consent, they may be separated if they wish
So much for 'in sickness and in health.'