Cedarhurst – this is the halacha that I was always taught. Immediately, for a man, three months for a woman. If widowed, the man has to wait for Shloshim to be over, I think. Otherwise, he can remarry right away. A woman always has to wait three months (even when elderly), presumably to ensure she is not with child by the other husband. The man does not have to wait, because al pi halacha before R’Gershom, he could have taken a second wife at any time, while married to the first.
If I am mistaken in any of the above, I am sure I will be corrected by eagle-eyed posters.