When a burial takes place, the flowers come to the cemetery or churchyard on the hearse. They are normally removed from the hearse and placed somewhere near the grave for the family and other mourners to look at following the service. When the grave is completed, they will be moved onto the grave and will remain there for a time. Each cemetery and churchyard will have different rules on how long floral tributes may remain, and you should enquire direct with them to establish this.
When a cremation takes place, the flowers will normally travel to the crematorium on the hearse. During the service, they will be taken on to the flower terrace, where they can be viewed following the service. Usually they will remain in place for a day or two until they are removed by the crematorium staff.
Your funeral director will normally offer you some options regarding flowers following the service. The options will differ depending on where the funeral has taken place.