In our council, any request for a dispensation is made via the clerk as soon as possible before the meeting, which is then discussed under declarations of interest at the meeting and a decision made.
Generally, applications may also be made at the council meeting itself if the council have a standing item on the agenda to deal with dispensation requests and the nature of the interest has only become apparent to a councillor at the meeting itself.
I don't know of any specific notice being required, (perhaps depends on your standing orders?)