Does the confirmation of a couple's calling and election happen right away if their marriage is right or do they go back at a later date and receive a confirmation by laying on of hands?
As to the time in which this blessing may be received, as a general statement
we may say that sufficient time (according to the Lord's own timetable and
infinite knowledge) must elapse before the couple can receive it. They must live the gospel, keep the commandments, experience a variety of circumstances in life--both good and bad--and regardless of those circumstances still live up to the covenants they have made before the Lord, exercising repentance whenever needed.
As you can imagine, this cannot happen overnight.
I am not at liberty to explain how a couple is sealed. Just as we do not describe the holy endowment--nor any other temple ordinance, for that matter--we do not describe this ordinance either. Sacred matters must be dealt with the utmost reverence and respect, and one should never publicize descriptions of temple ordinances.
One more thing: In your question you mention "... if their marriage is right ..." Let me add that only consistent effort on the part of both spouses can make a marriage "right," and that also takes time. Any marriage can be made right or wrong, although there are a few cases in which one doesn't need to be a "rocket scientist" to see that the odds of having a successful or failed marriage are quite visible from the time of the engagement. But even in these cases, no one can predict how people will use or misuse their agency in years to come.